Basic Topology |
Contents
Introduction 1 Eulers theorem | 1 |
Topological equivalence | 8 |
Surfaces 4 Abstract spaces 5 A classification theorem | 16 |
Copyright | |
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barycentric subdivision base point boundary circle called chain map choose closed surface coefficients combinatorial surface compact construction contains covering space curve cylinder defined definition denote dimension disc disjoint edge loop edge path element equivalent euclidean space Euler characteristic example Figure finite number fixed points free group fundamental group give given H₁(K Hausdorff space homeo homeomorphism homology groups homotopy type Hq(K identity induced infinite cyclic integer interior intersection isomorphic Klein bottle knot group lemma Möbius strip morphism neighbourhood nonempty one-one open cover open sets orbit space oriented q-simplex path-connected polygonal polyhedron Problems proof of theorem prove q-cycle real line result shown in Fig simplicial approximation simplicial complex simplicial map simply connected sphere subcomplex subgroup subset subspace Suppose topological group topological space topology torus triangulable space union v₁ vertex vertices Z₂