Lecturer(s)


AVERBUCH Vladimír, DrSc.

ROTH Samuel Joshua, Mgr. Ph.D.

Course content

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).

Learning activities and teaching methods

unspecified

Recommended literature


D. Krupka, O. Krupková. Topologie a geometrie, 1. Obecná topologie. SPN, Praha, 1989.

J. L. Kelley. General Topology. Van Nostrand, Princeton, 1957.

N. Bourbaki. Topologie générale.
