Syllabus
1. Metric, metric spaces, continuous and uniformly continuous mappings, homeomorphism, isometry. Open and closed sets, interion, closure, boundary. Subspace, sum and product of metric spaces.
2. Totally bounded and separable metric spaces.
3. Complete metric spaces, completion, Cantor theorem, Baire theorem.
4. Compact metric spaces, Cantors discontinuum, Hilbert cube.
5. Connected metric spaces.
6. Hausdorff metric.
Annotation
Non-obligatory course for the first year of study. The aim of this lecture is to provide several results about metric spaces that are deeper than in the basic course of mathematical analysis and to define some notions from topology.