Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course. As a text, the exposition in the earlier chapters proceeds at a pedestrian pace. A preliminary chapter covers those topics requisite to the main body of work.
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There are two introductions to general topology which are classics. Thsi book, Kelley, is the lighter one of them, while Engelking is the heavier one. Read full review
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accumulation point axiom of countability belongs Boolean cardinal number cartesian product Cauchy closed sets closed subset closure cluster point compact set compact space compact subset compactification complement Consequently contains continuous functions coordinate space countable base defined definition disjoint domain f equicontinuous equivalent family of sets finite intersection finite number follows Hausdorff space hence homeomorphic identical jointly continuous lemma linear locally compact locally finite maximal member of 11 metric space neighborhood system non-negative integers non-void open cover open set open subset ordinal pairs paracompact pointwise convergence product space product topology proposition pseudo-metric pseudo-metric space quotient space quotient topology real numbers real-valued function satisfies sequence space is complete subbase subcover subfamily subspace summable Suppose Theorem Let tion topological group topological space Tychonoff space uniform space uniformity 11 uniformly continuous union upper bound usual topology X X X