General Topology (WS 2010/2011)

Bibliography:

J. Dugundji, "Topology", Allyn and Bacon inc. (1966)

Any introductory book on General Topology

Diagram of the main classes of Topological Spaces discussed in class

Course outline (30 hours):

Topology. Basis and subbasis.

Open, closed sets. Interior, closure, derived, boundary of a set. Dense sets.

Continuous maps. Closed, open maps. Homeomorphisms. Local homeomorphisms are open.

The induced topology: subspaces.

The product topology.

The pull-back topology. Quotients. Homomorphism Theorem.

Connected spaces. Applications: Intermediate value Theorem, types of homeomorphisms of intervals.

Path-connected spaces. Locally connected spaces.

Separation Axioms. Urysohn's Lemma.

Compact spaces. Relatively compact subspaces. The finite intersection property.

Weierstrass Theorem. Compact Hausdorff spaces are normal.

Metric spaces. Metric spaces are normal.

Compactness in metric spaces: complete and totally bounded metric spaces, compact by sequences metric spaces.

Countable Axioms: 1st countable, 2nd countable, separable, Lindelöf spaces.

Locally compact spaces. Locally compact Hausdorff spaces are regular.

Compactifications. Alexandroff one-point compactification.

Letzte Änderung: 2. 2. 2011