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Math 344-1,2: Kursobjekt

Appendix D Topological specimens

1.1 Topological spaces

Topological specimen 1 Standard topology on \(\R\)
Topological specimen 2 Trivial and discrete topology
Topological specimen 3 Cofinite topology

1.2 Topological basis

Topological specimen 4 Lower limit topology
Topological specimen 5 \(K\)-topology
Topological specimen 6 Order topology

1.3 Metric spaces

Topological specimen 7 Metric spaces

1.5 Limit points and the Hausdorff property

Topological specimen 8 Zariski topology on \(\R^n\)

1.6 Subspaces and finite products

Topological specimen 9 Subspace
Topological specimen 10 Finite products

1.7 Arbitrary products

Topological specimen 11 Product space (arbitrary)

1.8 Convergence in product spaces

Topological specimen 12 Uniform topology

1.10 Homeomorphisms

Topological specimen 13 Coproduct space

1.11 Quotients

Topological specimen 14 Quotient space

1.13 Path-connected spaces

Topological specimen 15 Topologist’s sine curve

1.16 Compactness in metric spaces

Topological specimen 16 Cantor set

1.17 Locally compact spaces and compactification

Topological specimen 17 One-point compactification
Topological specimen 18 Stereographic projection

1.21 Urysohn offspring

Topological specimen 19 Space-filling curve