MU:MU03263 Chapters in Topology I

MU03263 Chapters in Topology I

Mathematical Institute in Opava
Winter 2015

Extent and Intensity

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

Guaranteed by

Vladimír Averbuch, DrSc.
Mathematical Institute in Opava

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. Filters (filter basis, trace of a filter, operations over filters, ultrafilters and their basic properties).
2. Filters and topologies (convergent filters, description of topologinal notions in terms of filters).
3. Separability (separability axioms, equivalent characterizations of Hausdorff separability, theorem on continuous extension).
4. Initial topology (definition and basic examples, description of initial topology in terms of filters, subspaces and products).
5. Compactness (equevalent characterizations of compactness, Tichonov 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

Czech

Further comments (probably available only in Czech)

The course can also be completed outside the examination period.