Ask a Topologist

Ask a Topologist was a forum to ask elementary or advanced questions in topology or related areas of topology, geometry, analysis and algebra. Dr. Henno Brandsma was the editor for this service. Some answers were collected at Topology Explained.

If you use answers from this forum and present them as your own in homework assignments or scholarly papers without clearly acknowledging Topology Atlas as the source, then you have plagiarized and may face disciplinary actions from your school.

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Topology Explained

Here are some topology teaching notes written by Henno Brandsma and Abhijit Dasgupta for Ask a Topologist.

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^ω; 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