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Topology Explained
This is a collection of notes on topics in topology.
These notes will be useful to people learing topology.
This collection is still being developed; please send us your lecture
notes or your suggestion for new notes.
These notes were written by Henno Brandsma and Abhijit Dasgupta for the
Topology Atlas Q+A Board.
- Axiom of choice
- A proof of Tychonoff
Theorem implies AC
- De Morgan in general and
choice
- Uniform spaces
- Some elementary facts on
uniform spaces
- Dimension
- A little overview of
dimension
- Normality, paracompactness, metrisability
- On paracompactness, full
normality and the like
- Proof of a lemma on
paracompactness plus applications
- Proof of the
Nagata-Smirnov metrisation theorem
- Paracompactness, covers
and perfect maps
- Useful theorems on normal
spaces
- The shrinking lemma
- Limit points of discrete
sets in metric spaces
- Connectedness
- Connectedness I
- Components in three
product topologies on R^\omega
- Boundaries, interiors and
open maps
- Compactness
- Covering maps and perfect
maps
- Nets, cluster points and
the Tychonoff theorem
- H-closed and not
compact
- Inverse limits,
compactness and why Hausdorffness is important
- Tychonoff and Kolmogorov
extension
- Compactness in
function spaces: Arzela-Ascoli type theorems
- Cardinal functions
- Arhangel'skii's theorem, a
proof
- Quotient maps
- Quotient maps
- General constructions
- Embeddings in to products
of the Sierpinski space
- The fourteen subsets
problem: interiors, closures and complements
- Countable metric spaces without isolated points
- Algebraic topology
- Checking all the axioms for
the first homotopy group
Revised: June 25, 2005.
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2003 by Topology Atlas.
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