Introduction to TopologyA 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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Introduction to Topology: Second Edition Theodore W. Gamelin,Robert Everist Greene Limited preview - 2013 |
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Axiom Baire Category Theorem Banach space barycentric subdivision base Cauchy sequence Choose closed sets closed subset closure cofinite topology coincides compact Hausdorff space connected component constant map continuous function converges countable covering map defined denoted dense differentiable disjoint open endpoints fixed Exercise exists exponential finite number fixed point function f fundamental group ƒ and g ƒ is continuous Hausdorff space Hence homeomorphic homotopy class identity map integer intersection inverse isomorphism Let f let ƒ limit points linear operator loop map f map ƒ nonempty obtain one-to-one open ball open cover open neighborhood open sets open subset path components path-connected Prove quotient space real numbers satisfies second-countable Section simplex simply connected space and let subspace Suppose topological space U₁ union unique V₁ vector field vector space X₁ y₁ zero α α