Introduction to Topology, Fall 2020, Universität Basel

Wednesday, 14.15-16.00 (Zoom)

Assistants: Julia Schneider, Pascal Fong, Shuta Nakajima

Literature:

Additionally: Tentative list of topics:

Lectures

16.09

Topological spaces: definition and basic examples (induced topology, trivial topology, discrete topology, Euclidean topology). Metric spaces: definition and examples. Metric topology. Continuous maps of topological spaces.

Video

23.09

Base and subbase of topology. Topology generated by base and subbase. Product topological space. Comparison of topologies (finer, coarser, equivalent).

Video

30.09

Interior, exterior, and boundary of a set. Giving topology via closed sets. Zariski topology. Closure, limit points. Dense subsets.

Video

07.10

Hausdorff spaces. Examples and non-examples. A space is Hausdorff iff the diagonal is closed. Separation axioms T0-T4. Zariski topology on the spectrum of a commutative ring. Normal and regular spaces.

Video

14.10

Normal and regular spaces. Second-countable spaces. Metrizable spaces, Urysohn's metrization theorem (statement). Tychonoff topology, its base and subbase. Countable product of metrizable spaces is metrizable. Hilbert cube.

Video