Introduction to General Topology |
Contents
Logical Warmup | 1 |
Contents | 3 |
Preliminaries | 26 |
What is Topology? | 61 |
Basic Concepts | 104 |
Spaces with Special Properties | 132 |
Separation Axioms | 149 |
Products and Coproducts | 189 |
Complete Metric Spaces | 276 |
Some Applications | 287 |
Completions of a Metric | 302 |
Uniform Spaces | 339 |
Selected Topics | 364 |
Miscellaneous Exercises | 394 |
| 401 | |
| 405 | |
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Common terms and phrases
argument axioms B₁ base bijection bounded called Chapter characterisation closed sets closed subset closure cluster point compact space compactification concept continuous function converges Corollary defined definition denoted dense discrete space element empty set equivalence relation euclidean spaces example Exercise filter finite intersections follows function f functor ƒ is continuous geometry given Hausdorff space hence Hint homeomorphic implies indexed family induced lemma Let f Lindelöff locally connected logical mathematics metric space morphism neighbourhood non-empty Notes and Guide objects open balls open cover open interval open sets open subset partially ordered product topology proof Proposition Prove pseudometric quotient space reader real line real numbers relative topology result second countable semi-open interval statement sub-base subspace suppose T₁ T2 space theorem tion topological product topological space trivial Tychonoff Tychonoff space uniform space union unique unit interval usual topology X₁