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Metric Topology 42 Metric Topology
Metric Space Properties Chapter 3 Metric Space Properties
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1-sphere a e d abelian accumulation point adjunction space automorphism base basepoint bijection called Cantor's closed sets closed subsets closed subspace closure CLS(A cofibration compact subspace compactification complement connected subspace Construct contains continuous function Corollary covering projection covering space CW complex defined deformation retract denoted dense disc disjoint union edges endpoints Euclidean Example Exercise exists foliation function F fundamental group Hausdorff space hence homeomorphic homotopy equivalent identification map infinite integers intersection inverse isomorphism knot Lemma lifting locally compact loop metric subspace morphism non-cut points nonempty open covering open interval open neighborhood open sets open subsets ordinal pair paracompact partition path path-components path-connected plane point x e polygonal pre-image Proof Prove quotient space real number second countable Section sequentially compact simply connected covering subgroup surface ternary Theorem Let topological product topological space torus unique weak topology