Courier Corporation, 12 juil. 2012 - 384 pages
Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340 exercises in all). The text's value as a reference work is enhanced by a collection of historical notes, a bibliography, and index. 1970 edition. 27 figures.
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algebraic Amer axiom of choice basic nhood Cauchy closed sets closed subset closure cluster point collection compact spaces compact subset compact—open topology compactiﬁcation completely regular connected space continuous functions continuous map continuum converges deﬁned Deﬁnition denote dense disjoint open sets elements embedded equivalent example Exercise f is continuous ﬁlter ﬁnd ﬁrst countable ﬁxed function f Hausdorff space Hausdorll hence homeomorphic homotopy iﬁ iﬂ inﬁnite intersection interval Lemma Let f Lindelof linear locally compact locally connected map f Math metrization theorem nhood nhood base nonempty normal spaces one—one open cover open set paracompact space pointwise product space Proof proved Proximity Spaces pseudometric quotient real-valued functions result retract Section sequence subbase subspace Suppose T1-space topological space topology induced totally bounded Tychonoff space Uber ultraﬁlter uniform cover uniform space uniformly continuous union Urysohn usual topology weak topology