@ARTICLE {TP33.01, 
AUTHOR = {Uspenskij, Vladimir}, 
TITLE = {On extremely amenable groups of homeomorphisms}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {1--12}, 
URL = {}, 
MRCLASS = {54H11 (22A05 22A15 22F05 37B05 54H15 54H20 54H25 57S05)}, 
KEYWORDS = {greatest ambit, minimal flow, Vietoris topology, exponent},
ABSTRACT = {A topological group $G$ is {\em extremely amenable} if every
compact $G$-space has a $G$-fixed point. Let $X$ be compact and
$G \subset \text{Homeo}(X)$. We prove that the following are equivalent: 
(1) $G$ is extremely amenable; (2) every minimal closed $G$-invariant 
subset of $\text{Exp} R$ is a singleton, where $R$ is the closure of the 
set of all graphs of $g \in G$ in the space $\text{Exp} (X^2)$ 
($\text{Exp}$ stands for the space of closed subsets); (3) for each
$n = 1, 2, \dots$ there is a closed $G$-invariant subset $Y_n$ of 
$(\text{Exp} X)^n$ such that $\cup_{n=1}^\infty Y_n$ contains arbitrarily 
fine covers of $X$ and for every $n \ge 1$ every minimal closed 
$G$-invariant subset of $\Exp Y_n$ is a singleton. This yields an 
alternative proof of Pestov's theorem that the group of all 
order-preserving self-homeomorphisms of the Cantor middle-third set (or of
the interval $[0,1]$) is extremely amenable.},
} 
@ARTICLE {TP33.02, 
AUTHOR = {Arhangel'skii, A.V.}, 
TITLE = {Some aspects of topological algebra and remainders of topological groups}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {13--28}, 
URL = {}, 
MRCLASS = {54A25 (54B05)}, 
KEYWORDS = {remainder, compactification, topological group, semitopological group, paratopological group, $p$-space, $D$-space, homogeneous space, metrizability, countable type, $\pi$-character, $\pi$-base}, 
ABSTRACT = {In the Introduction a very brief survey of some classical
results and ideas of topological algebra is given. The principal interest
in the article is directed at remainders of topological groups; here some
new results are obtained. Thus, we continue the research line adopted in
[A.V. Arhangel'skii, {\em Remainders in compactifications and 
generalized metrizability properties}, {\em More on remainders close to 
metrizable spaces}, {\em On first countable remainders}, {\em Two types 
os remainders of topological groups}]. Several results
from these articles are improved. It is established that if a remainder of
a non-locally compact topological group $G$ is the union of a finite
collection of metrizable spaces, then $G$ is metrizable. A far reaching
generalization of this result is also given; it is based on the notion of
a $D$-space. If $X$ is an uncountable Tychonoff space, and $bY$ is a
Hausdorff compactification of the space $Y=C_p(X)$ such that the remainder
$bY \setminus Y$ is homogeneous, then $bY$ can be mapped continuously onto
the Tychonoff cube $I^{\omega _1}$. Some further results and open problems
on remainders of topological groups are provided.},
} 
@ARTICLE {TP33.03, 
AUTHOR = {Glasner, Eli}, 
TITLE = {On two problems concerning topological centers}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {29--39}, 
URL = {}, 
MRCLASS = {54H20 (22A15)}, 
KEYWORDS = {topological center, \v{C}ech-Stone compactification, Ellis group, distal systems}, 
ABSTRACT = {Let $\Gamma$ be an infinite discrete group and $\beta\Gamma$ 
its \v{C}ech-Stone compactification. Using the well known fact that a free 
ultrafilter on an infinite set is nonmeasurable, we show that for each 
element $p$ of the remainder $\beta\Gamma \setminus \Gamma$, left 
multiplication $L_p:\beta\Gamma \to \beta\Gamma$ is not Borel measurable.
Next assume that $\Gamma$ is abelian. Let $\mathcal{D} \subset 
\ell^\infty(\Gamma)$ denote the subalgebra of distal functions on $\Gamma$ 
and let $D = \Gamma^\mathcal{D} = |\mathcal{D}|$ denote the corresponding 
universal distal (right topological group) compactification of $\Gamma$.
Our second result is that the topological center of $D$ (i.e., the set of 
$p \in D$ for which $L_p:D \to D$ is a continuous map) is the same as the 
algebraic center and that for $\Gamma = \mathbb{Z}$, this center coincides
with the canonical image of $\Gamma$ in $D$.}, 
} 
@ARTICLE {TP33.04, 
AUTHOR = {Spreen, Dieter}, 
TITLE = {A construction method for partial metrics}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {41--54}, 
URL = {}, 
MRCLASS = {54E15 (06B35 54E25 54E35 68Q55)}, 
KEYWORDS = {partial metric, quasi-uniformity, asymmetric topology, domain theory}, 
ABSTRACT = {We present a general construction that starts from a family of
interior-preserving open coverings of a given subspace and results in a
partial metric with respect to which all subspace elements have
self-distance zero. A necessary and sufficient condit ion is derived for
when this partial metric induces the given topology. The condition is
particularly satisfied if the members of each covering are pairwise
disjoint.

The method is based on Fletcher's universal construction for transitive
quasi-uniformities. Important examples of partial metrics in the
literature can be obtained in this way.

As a consequence of the construction, the set of all points with
self-distance zero is a $G_\delta$. Moreover, this subspace is
zero-dimensional in its induced topology.}, 
}
@ARTICLE {TP33.05, 
AUTHOR = {De, Dibyendu and Hindman, Neil and Strauss, Dona}, 
TITLE = {Sets central with respect to certain subsemigroups of $\beta S_d$}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {55--79}, 
URL = {}, 
MRCLASS = {54D35 (22A15 05D10 54D80)}, 
KEYWORDS = {central sets, compact subsemigroups, image partition regular matrices}, 
ABSTRACT = {\emph{Central} sets in a semigroup $S$ are most simply
characterized as members of minimal idempotents in the Stone-\v{C}ech
compactification $\beta S_d$ of $S$ with the discrete topology. They are
known to have remarkably strong combinatorial properties. In this paper
we concentrate on members of idempotents in compact subsemigroups $T$ of
$\beta S_d$. We show that under reasonable hypotheses any member of a
minimal idempotent in $T$ is in fact a member of many distinct minimal
idempotents in $T$. And we show that under certain assumptions which occur
quite widely, the subsets of $S$ whose closures contain $T$ must contain
images of all first entries matrices. For example, all of our results
apply to the case in which $(S,+)$ is a commutative cancellative
topological semigroup with an identity and $T$ is the set of ultrafilters
on $S$ which converge to the identity.},
} 
@ARTICLE {TP33.06, 
AUTHOR = {D\'{\i}az, Raquel and Ushijima, Akira}, 
TITLE = {On the properness of some algebraic equations appearing in Fuchsian groups}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {81--106}, 
URL = {}, 
MRCLASS = {20H10 22E40 (32G15)}, 
KEYWORDS = {Fuchsian groups, fundamental polygons}, 
ABSTRACT = {In this paper we give necessary and sufficient conditions on 
three orientation-preserving hyperbolic isometries $T_1,T_2,T_3$ so that
for any point $x \in \mathbb{H}^2$ the orthogonal bisectors of the three 
segments with endpoints $x,T_i(x)$ intersect. This is equivalent to 
proving the properness of certain algebraic sets. As a corollary, we give 
a new proof for the existence and density of generic fundamental polygons 
for cocompact Fuchsian groups.}, 
} 
@ARTICLE {TP33.07, 
AUTHOR = {Fla\v{s}kov\'{a}, Jana}, 
TITLE = {Ideals and sequentially compact spaces}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {107--121}, 
URL = {}, 
MRCLASS = {54G99 03E50 (54H05 05C55)}, 
KEYWORDS = {sequentially compact space, van der Waerden space, Hindman space, $F_{\sigma}$-ideal},
ABSTRACT = {We say that a topological space $X$ is an 
$\mathcal{I}_{\frac1n}$-space if for every sequence $\langle x_n 
\rangle_{n \in \mathbb{N}}$ in $X$ there exists a converging subsequence 
$\langle x_{n_k} \rangle _{k \in \mathbb{N}}$ with $\sum_{k \in 
\omega}\frac{1}{n_k} = \infty$. Every 
$\Sm$-space is sequentially compact, but not every
sequentially compact space is $\mathcal{I}_{\frac1n}$-space.

Assuming Martin's axiom for $\sigma$-centered posets we construct a
van der Waerden space that is not an $\mathcal{I}_{\frac1n}$-space and an 
$\mathcal{I}_{\frac1n}$-space that is not Hindman.},
}
@ARTICLE {TP33.08, 
AUTHOR = {Kada, Masaru}, 
TITLE = {How many miles to $\beta\omega$? II --- non-rapid ultrafilters and Higson compactifications}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {123--129}, 
URL = {}, 
MRCLASS = {03E17 (03E35, 54D35)}, 
KEYWORDS = {Higson compactification, Stone-\v{C}ech compactification, rapid ultrafilter}, 
ABSTRACT = {We prove the following theorem: If there is a base $\mathcal{F}$ 
of a non-rapid ultrafilter on $\omega$, then we can approximate 
$\beta\omega$ by $|\mathcal{F}|$-many Higson compactifications of $\omega$ 
in a nontrivial way.}, 
} 
@ARTICLE {TP33.09, 
AUTHOR = {Brosowski, B. and da Silva, A.R.}, 
TITLE = {On partitions of unity in the Dedekind completion of certain subsets of continuous functions}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {131--138}, 
URL = {}, 
MRCLASS = {54D35 (32A70)}, 
KEYWORDS = {partitions of unity, Dedekind completion}, 
ABSTRACT = {In this short paper we prove the existence of a continuous 
partition $\sum\limits_{\nu=1}^n \rho_\nu=1$ in the Dedekind-completion of 
a subspace $Z$ of $C(T,\mathbb{R})$, where the functions $\rho_\nu$ are 
constant on certain $X$-antisymmetric sets, where $Z = \text{span}(X \cup 
X^2)$. Further, we present some applications of our technique.},
} 
@ARTICLE {TP33.10, 
AUTHOR = {Szyma\'nski, Jerzy}, 
TITLE = {On some applications of equivalence relations in topological dynamics}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {139--152}, 
URL = {}, 
MRCLASS = {37B05 (37B40 37-02 37-06)}, 
KEYWORDS = {equivalence relations, extreme relations, deterministic extensions, Kolmogorov extensions, asymptotic pairs}, 
ABSTRACT = {We discuss some applications of equivalence relations in 
topological dynamics. We look at their use in defining some topological 
objects (topological determinism and Kolmogorov property) and their 
applications in proofs of properties of these objects.},
} 
@ARTICLE {TP33.11, 
AUTHOR = {van Mill, Jan}, 
TITLE = {Homogeneous spaces and transitive actions by $\aleph_0$-bounded groups},
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {153--161}, 
URL = {}, 
MRCLASS = {22F05 57S05 22F30 (03E15)}, 
KEYWORDS = {topological group, transitive action, Polish space}, 
ABSTRACT = {We construct a homogeneous connected Polish space $X$ on which no
$\aleph_0$-bounded topological group acts transitively. In fact, $X$
is homeomorphic to a convex subset of Hilbert space $\ell^2$.},
} 
@ARTICLE {TP33.12, 
AUTHOR = {Ostrovskii, M.I.}, 
TITLE = {Coarse embeddability into Banach spaces}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {163--183}, 
URL = {}, 
MRCLASS = {54E40 46B20 (05C12)}, 
KEYWORDS = {coarse embedding, uniform embedding, Banach space, expander graph, locally finite metric space, bounded geometry}, 
ABSTRACT = {The main purposes of this paper are (1) To survey the area of
coarse embeddability of metric spaces into Banach spaces, and, in 
particular, coarse embeddability of different Banach spaces into each 
other; (2) To present new results on the problems: (a) Whether coarse 
non-embeddability into $\ell_2$ implies presence of expander-like 
structures? (b) To what extent $\ell_2$ is the most difficult space to 
embed into?},
} 
@ARTICLE {TP33.13, 
AUTHOR = {Filali, Mahmoud and Vedenjuoksu, Tero}, 
TITLE = {Extreme non-Arens regularity of semigroup algebras}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {185--196}, 
URL = {}, 
MRCLASS = {43A20, 43A10(22A15)}, 
KEYWORDS = {extreme non-Arens regular, weakly almost periodic, slowly oscillating functions, semigroup algebra}, 
ABSTRACT = {Let $S$ be an infinite, discrete, weakly cancellative semigroup,
$\ell^\infty(S)$ the space of bounded functions on $S$, and 
$\text{WAP}(S)$ the subspace of weakly almost periodic functions. 
Then the quotient space $\ell^\infty(S)/\text{WAP}(S)$ contains an 
isometric linear copy of $\ell^\infty(S)$. This implies that the 
semigroup algebra $\ell^1(S)$ is extremely non-Arens regular.},
} 
@ARTICLE {TP33.14, 
AUTHOR = {B\`es, Juan}, 
TITLE = {Geometric characteristics and common hypercyclic subspaces}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {107--209}, 
URL = {}, 
MRCLASS = {47A16}, 
KEYWORDS = {hypercyclic and universal vectors}, 
ABSTRACT = {We consider geometric characteristics of countably many 
hypercyclic operators on a Banach space and study their effect on the 
existence of common hypercyclic subspaces.},
} 
@ARTICLE {TP33.15, 
AUTHOR = {Altay U\u{g}ur, Ay\c{s}eg\"{u}l and Diker, Murat}, 
TITLE = {A note on ditopological texture spaces}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {211--223}, 
URL = {}, 
MRCLASS = {54E55}, 
KEYWORDS = {texturing, texture space, ditopology, plain texture, induced subtexture, complete biregularity}, 
ABSTRACT = {In this study, we present the hereditary separation 
properties of plain ditopological texture spaces for induced subtextures. 
Brown and his team proved that the complete biregularity is productive. 
Here, using the concept of induced subtexture, we show that the converse 
of this result is true for plain texture spaces, namely if a product of 
plain ditopological texture spaces is completely biregular, then all 
factor spaces are also completely biregular.},
} 
@ARTICLE {TP33.16, 
AUTHOR = {Hofmann, Karl H. and Morris, Sidney A.}, 
TITLE = {Contributions to the structure theory of connected pro-Lie groups}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {225--237}, 
URL = {}, 
MRCLASS = {22A05}, 
KEYWORDS = {connected pro-Lie group, SIN-group, MAP-group, Baire space, just-non-Lie group},
ABSTRACT = {We present some recent results in the structure theory
of pro-Lie groups and locally compact groups, improvements of known 
results, and open problems.},
}
@ARTICLE {TP33.17, 
AUTHOR = {Herrlich, Horst and Keremedis, Kyriakos and Tachtsis, Eleftherios}, 
TITLE = {On super second countable and super separable metric spaces}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {239--249}, 
URL = {}, 
MRCLASS = {03E25 54A35 (54D65 54D70 54E35)}, 
KEYWORDS = {axiom of choice, weak axioms of choice, second countable metric spaces, super second countable metric spaces, separable metric spaces, super separable metric spaces},
ABSTRACT = {In the framework of ZF (i.e., Zermelo-Fraenkel set theory 
without the Axiom of Choice) we show that: (1) Every super second 
countable metric space is super separable. (2) Every super second 
countable metric space is hereditarily super second countable.
The above results answer related questions from Gutierres ``On 
first and second countable spaces and the axiom of choice".
We also show that the axiom $\text{CAC}(\mathbb{R})$ (i.e., the Axiom of 
Choice restricted to countable families of non-empty subsets of reals)
is equivalent to the converse of (1) and to the corresponding statement 
of (2) for super separable metric spaces.}, 
}
@ARTICLE {TP33.18, 
AUTHOR = {Curry, Clinton P.}, 
TITLE = {Recognizing indecomposable subcontinua of surfaces from their complements}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {251--268}, 
URL = {}, 
MRCLASS = {54F15 (57N05)}, 
KEYWORDS = {indecomposable continuum, complementary domain, closed surface, double-pass condition},
ABSTRACT = {We prove two theorems which allow one to recognize
indecomposable subcontinua of closed surfaces without boundary. If $X$ is
a subcontinuum of a closed surface $S$, we call the components of $S
\setminus X$ the \emph{complementary domains of $X$}. We prove that a
continuum $X$ is either indecomposable or the union of two indecomposable
continua whenever it has a sequence $(U_n)_{n=1}^{\infty}$ of distinct 
complementary domains such that $\lim_{n \rightarrow \infty} \partial U_n 
= X$. We define a slightly stronger condition on the complementary 
domains of $X$, called the \emph{double-pass condition}, which we 
conjecture is equivalent to indecomposability. We prove that this is so 
for continua which are not the boundary of one of their complementary 
domains.},
}
@ARTICLE {TP33.19, 
AUTHOR = {Luk\'acs, G\'abor}, 
TITLE = {Hereditarily non-topologizable groups}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {269--275}, 
URL = {}, 
MRCLASS = {20F05, 22C05(22A05, 54H11)}, 
KEYWORDS = {non-topologizable, $c$-compact, topological group, hereditarily non-topologizable, totally minimal, small invariant neighborhoods, torsion group},
ABSTRACT = {A group $G$ is {\em non-topologizable} if the only Hausdorff 
group topology that $G$ admits is the discrete one. Is there an infinite 
group $G$ such that $H/N$ is non-topologizable for every subgroup $H \leq 
G$ and every normal subgroup $N \vartriangleleft H$? We show that an 
answer to this essentially group theoretic question provides a solution to 
the problem of $c$-compactness.},
}
@ARTICLE {TP33.20, 
AUTHOR = {Dow, Alan and Pichardo-Mendoza, Roberto}, 
TITLE = {Efimov spaces, CH, and simple extensions}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {277--283}, 
URL = {}, 
MRCLASS = {54A25(5AD30, 04A15)}, 
KEYWORDS = {Efimov space, CH},
ABSTRACT = {We give a construction under CH of an inverse system of 
simple extensions so that its limit is an Efimov space. This example 
shows that CH alone implies that a conjecture of Mercourakis about 
measures is false.},
}
@ARTICLE {TP33.21, 
AUTHOR = {Georgiou, D.N. and Iliadis, S.D. and Megaritis, A.C.}, 
TITLE = {On positional dimension-like functions}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {285--296}, 
URL = {}, 
MRCLASS = {54B99, 54C25}, 
KEYWORDS = {dimension theory, positional dimension-like function},
ABSTRACT = {In [S.D. Iliadis, {\em Universal spaces and mappings}] the so 
called positional dimension-like functions of the type ind were 
introduced. These functions were studied only with respect to the property 
of universality. Here, we first give some relations between positional 
dimension-like functions of the type ind and then study these functions 
with respect to other standard properties of dimension theory.},
}
@ARTICLE {TP33.22, 
AUTHOR = {Claes, Veerle}, 
TITLE = {Coreflective subconstructs of the constructs of affine sets}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {297--317}, 
URL = {}, 
MRCLASS = {54A05, 54B30, 18B99}, 
KEYWORDS = {affine set, hereditary coreflective subconstruct, initially dense object, metrically generated theory, $(\\mathbb{T},\mathsf{V})$-category},
ABSTRACT = {For a topological construct, we give necessary and sufficient 
conditions to be isomorphic to a coreflective subconstruct of a category 
of affine sets. This means that the objects can be described 
isomorphically as sets structured by a collection of functions. We also 
characterize the hereditary coreflective subconstructs of the categories 
of affine sets and the subcategories constructed from an algebra 
stucture. We prove that these two types of subconstructs do not coincide. 
As an application of these results we find a relation between the affine 
sets over $[0, \infty]$ and the metrically generated categories. 
Finally, we will give some examples of 
$(\mathbb{T},\mathsf{V})$-categories which can be embedded in the category 
of affine sets over $\mathsf{V}$.},
}
@ARTICLE {TP33.23, 
AUTHOR = {\'{A}gueda, Raquel}, 
TITLE = {Slices on the boundary of Schottky space of genus 2}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {319--341}, 
URL = {}, 
MRCLASS = {30F40, 32G15}, 
KEYWORDS = {Kleinian groups, Teichm\"{u}ller theory},
ABSTRACT = {Let $\mathcal{R}$ be the deformation space of free Kleinian groups
generated by a parabolic and a loxodromic element, which correspond to 
representations into $\text{PSL}(2,\mathbb{C})$ of the fundamental group 
of a doubly cusped handlebody $M$ whose boundary surface is a twice 
punctured torus. In this paper we show that this parameter space appears 
as the natural generalization of $1$-complex dimensional slices which lie 
on its boundary: the Maskit embedding of a once punctured torus and the 
Riley slice of a four punctured sphere.},
}
@ARTICLE {TP33.24, 
AUTHOR = {Tsereteli, I. and Zambakhidze, L.}, 
TITLE = {Metrizability and dimension}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {343--359}, 
URL = {}, 
MRCLASS = {54F45}, 
KEYWORDS = {dimension functions, separable, metrizable, space},
ABSTRACT = {It is proved that under some natural restrictions any 
topologically closed subclass of the class of all Tychonoff spaces, 
where the three classical dimension functions coincide, is a subclass of 
the class of all metrizable spaces with a countable base providing a 
complete solution for a problem of A.V. Arhangel'skii, next to a 
partial solution of L.A. Tumarkin's problem.},
}
@ARTICLE {TP33.25, 
AUTHOR = {Grinblat, L.\v{S}.}, 
TITLE = {Theorems with uniform conditions on sets not belonging to algebras}, 
ISSN = {0146-4124}, 
JOURNAL = {Topology Proc.}, 
VOLUME = {33}, 
YEAR = {2009}, 
NUMBER = {}, 
PAGES = {361--380}, 
URL = {}, 
MRCLASS = {03E05 (54D35)}, 
KEYWORDS = {algebra on a set, ultrafilter, a set not belonging to algebras, pairwise disjoint sets, systems of distinct representatives},
ABSTRACT = {Let $\{\mathcal{A}_\lambda\}_{\lambda \in \Lambda}$ be a 
family of $\sigma$-algebras on a set $X$, where $\left|\Lambda\right| = 
\aleph_0$, with $\mathcal{A}_\lambda \neq {\mathcal{P}}(X)$ for any 
$\lambda \in \Lambda$, and for any finite set $J \subset \Lambda$, where 
$\left|J\right| = h \geq 3$, there exist $2h-2$ pairwise disjoint sets 
belonging to $\mathcal{P}(X) \setminus \bigcap_{\lambda \in J}
\mathcal{A}_\lambda$; then $\bigcup_{\lambda \in \Lambda} 
\mathcal{A}_\lambda \neq \mathcal{P}(X)$. 
If we substitute the estimate $2h-3$ for $2h-2$, this theorem does not hold.},
}