Armstrong, M.A.
Basic topology/
M.A. Armstrong
- New York: Springer, 1983.
- xii, 251 p. : ill. ; 25 cm.
- (Undergraduate texts in mathematics) .
1. Introduction --
1.1 Euler's theorem --
1.2 Topological equivalence --
1.3 Surfaces --
1.4 Abstract spaces --
1.5 A classification theorem --
1.6 Topological invariants --
2. Continuity --
2.1 Open and closed sets --
2.2 Continuous functions --
2.3 A space-filling curve --
2.4 The Tietze extension theorem --
3. Compactness and connectedness --
3.1 Closed bounded subsets of E[n] --
3.2 The Heine-Borel theorem --
3.3 Properties of compact spaces --
3.4 Product spaces --
3.5 Connectedness --
3.6 Joining points by paths --
4. Identification spaces --
4.1 Constructing a Möbius strip --
4.2 The identification topology --
4.3 Topological groups --
4.4 Orbit spaces --
5. The fundamental group --
5.1 Homotopic maps --
5.2 Construction of the fundamental group --
5.3 Calculations --
5.4 Homotopy type --
5.5 The Brouwer fixed-point theorem --
5.6 Separation of the plane --
5.7 The boundary of a surface --
6. Triangulations --
6.1 Triangulating spaces --
6.2 Barycentric subdivision --
6.3 Simplicial approximation --
6.4 The edge group of a complex --
6.5 Triangulating orbit spaces --
6.6 Infinite complexes --
7. Surfaces --
7.1 Classification --
7.2 Triangulation and orientation --
7.3 Euler characteristics --
7.4 Surgery --
7.5 Surface symbols --
8. Simplicial homology --
8.1 Cycles and boundaries --
8.2 Homology groups --
8.3 Examples --
8.4 Simplicial maps --
8.5 Stellar subdivision --
8.6 Invariance --
9. Degree and Lefschetz number --
9.1 Maps of spheres --
9.2 The Euler-Poincaré formula --
9.3 The Borsuk-Ulam theorem --
9.4 The Lefschetz fixed-point theorem --
9.5 Dimension --
10. Knots and covering spaces --
10.1 Examples of knots --
10.2 The knot group --
10.3 Seifert surfaces --
10.4 Covering spaces --
10.5 The Alexander polynomial --
Appendix: Generators and relations.
9780387908397
Topology
Mathematics
514 / ARM/