Introduction to Topology
A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations. Index. 51 illustrations.
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2ero ahove algehraic Axiom Baire Category Theorem Banach space Cauchy sequence Choose closed sets closed suhset closure cofinite topology coincides compact Hausdorff space compact space compact suhset connected component constant map continuous function contractihle converges convex comhinations corresponding countahle covering map defined hy definition denoted hy dense differentiahle disjoint open endpoints fixed equivalence class estahlishes Exercise exists exponential finite numher fixed point fundamental group given hy harycentric suhdivision hasic Hausdorff space helongs Hence homeomorphism homotopy class hoth identity map integer intersection inverse isomorphism Jacohian Lemma limit points linear operator loop nonempty ohserve one-to-one open cover open hall open neighhorhood open sets open suhset path components path-connected product topology prohlems Prove quotient space real numhers satisfies Section separahle simplex simply connected space and let suhcover suhsequence suhspace Suppose topological space totally hounded union unique unit hall vector field vector space