Author | Singer, I. M. author |
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Title | Lecture Notes on Elementary Topology and Geometry [electronic resource] / by I. M. Singer, J. A. Thorpe |
Imprint | New York, NY : Springer New York, 1967 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-7347-0 |
Descript | VIII, 232 p. online resource |
1 Some point set topology -- 1.1 Naive set theory -- 1.2 Topological spaces -- 1.3 Connected and compact spaces -- 1.4 Continuous functions -- 1.5 Product spaces -- 1.6 The Tychonoff theorem -- 2 More point set topology -- 2.1 Separation axioms -- 2.2 Separation by continuous functions -- 2.3 More separability -- 2.4 Complete metric spaces -- 2.5 Applications -- 3 Fundamental group and covering spaces -- 3.1 Homotopy -- 3.2 Fundamental group -- 3.3 Covering spaces -- 4 Simplicial complexes -- 4.1 Geometry of simplicial complexes -- 4.2 Barycentric subdivisions -- 4.3 Simplicial approximation theorem -- 4.4 Fundamental group of a simplicial complex -- 5 Manifolds -- 5.1 Differentiable manifolds -- 5.2 Differential forms -- 5.3 Miscellaneous facts -- 6 Homology theory and the De Rham theory -- 6.1 Simplicial homology -- 6.2 De Rhamโs theorem -- 7 Intrinsic Riemannian geometry of surfaces -- 7.1 Parallel translation and connections -- 7.2 Structural equations and curvature -- 7.3 Interpretation of curvature -- 7.4 Geodesic coordinate systems -- 7.5 Isometries and spaces of constant curvature -- 8 Imbedded manifolds in R3