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The Basic Constructs
Connectedness and Compactness
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2-manifold basis Cantor set cell cellular chainable Chapter cluster point compact metric space compact subset complementary domain complete component connected space continuous function continuous map continuum converges Corollary covering space defined Definition denote disjoint open disk element embedding end points equivalent example Exercise filter finite number finite subcover fundamental group Furthermore hence homeo homeomorphic homotopy induced integer inverse system isomorphic Lemma locally compact locally connected locally finite loop morphism n-cell neighborhood nonempty normal space Note obtained open cover open set open subset paracompact path connected plane problem product topology Proof reader relative topology result retract second countable Section separable sequence Show simple chain simple closed curve simplex simplicial complex simply connected subcomplex subspace Suppose that G Suppose that X,d T2 space topological space triangulation union usc decomposition vertex vertices weak topology