Fundamentals of Topology |
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Contents
Introduction | 1 |
Connectivity Properties | 85 |
Metrization | 101 |
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arcwise connected axioms B₁ B₂ base Bolzano-Weierstrass property C₁ C₂ Cauchy sequence closed subsets collection collectionwise normal compact subspace completely normal connected iff contains converges countably compact define DEFINITION denote dense discrete disjoint equivalence relation EXAMPLE EXERCISES F₁ F₂ finite subcover fixed-point property G₁ G₂ H₁(S Hausdorff space Hence homeomorphic homology theory homotopically equivalent homotopy identity mapping iff there exists implies integer intersection isomorphism lemma Let f Let G Lindelöf locally connected metric space modulo Moreover nonempty open cover open sets pair mapping paracompact partially ordered pathwise connected Proof Prove Theorem pseudometric quotient reader real numbers retract S₁ S₂ screenable second countable sequentially compact Show singular homology subbase t₁ T₁-space t₂ To-space topological space topology totally bounded U₁ uniform space x₁ П₁