Topology Proceedings
Document # baal-20
Topology Proceedings 26 No. 1 (2001-2002), pp. 255-270 |
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n-fold hyperspaces, cones and products
Sergio Mac\iias and Sam B. Nadler, Jr.
iven a continuum X and an integer n greater than one,
we consider the n-fold hyperspace, Cn(X), of X. We show
that if X is finite dimensional, then Cn(X) is not
homeomorphic to Cone(X). We also show that if X is hereditarily
indecomposable, then Cn(X) is not homeomorphic to the
Cone(Z) for any finite-dimensional continuum Z.
On the other hand, we show that if S1 is the unit circle, then
C2(S1) isnot homeomorphic to the product, Y×D, for
any one-dimensional continuum D.
Keywords: absolute neighborhood retract, absolute retract, Cantor
manifold, continuum, decomposable continuum, hereditarily indecomposable
continuum, hyperspace, indecomposable continuum, n-fold hyperspace,
n-fold symmetric product, terminal continuum, unicoherent continuum.
Mathematics Subject Classification: 54B20
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Topology Proceedings,
Volume 26 No. 1 (2001-2002)
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Date: November 1, 2002.