MU:MU03264 Chapters in Topology II

MU03264 Chapters in Topology II

Mathematical Institute in Opava
Summer 2018

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Guaranteed by

Vladimír Averbuch, DrSc.
Mathematical Institute in Opava

Prerequisites (in Czech)

MU03252 Chapters in Topology I || MU03263 Chapters in Topology I

Course Enrolment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

fields of study / plans the course is directly associated with

Course objectives

Repetition and deepening of some chapters of usual course of topology. Some further chapters.

Syllabus

1. Uniform spaces (multi-valued functions, entourages, induced topology, uniform continuity).
2. Complete spaces and completion (Cauchy filters, minimal Cauchy filters, completeness, theorem on completion, completeness and completion of subspaces and products).
3. Compactness and uniform structure (uniformity of compact spaces, pre-compactness, compactness of uniform spaces, compact sets in uniform spades).
4. Stone-Čech theorem (evaluation mapping, compactification, Stone-Čech theorem).
5. Ascoli theorem (uniform convergence, equi-continuity, Ascoli theorem).

Literature

recommended literature

N. Bourbaki. Topologie générale. info
D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989. info
J. L. Kelley. General Topology. Van Nostrand, Princeton, 1957. info

Language of instruction

English

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.