General Topology

Course code

MLM6225.DT

old course code

Course title in Estonian

Üldine topoloogia

Course title in English

General Topology

ECTS credits

3.0

Assessment form

assessment

lecturer of 2023/2024 Spring semester

Mart Abel (language of instruction:Estonian)

lecturer of 2024/2025 Autumn semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

Course aims

The aim of the course is to introduce the main concepts of topology and to give an overview of topological spaces, which are used more frequently.

Brief description of the course

The topics of this course are: Set theoretical definition of topology. Open and closed sets. Topological space. Examples. Neighbourhoods of points in a topological space. Closure, interior and cover of a set. Basis and subbasis of a topology. Defining topology by its basis or subbasis. Subspace of a topological space. Subspace topology. Quotient space of a topological space. Quotient topology. Product of topological spaces. Product topology. Continuity of maps in topological spaces. Open and closed maps. Homeomorphisms. Sequences and families. Convergence in topological spaces. “Analysis situs”- historical geometric interpretation of topology. Metrics and norm. Metric spaces and normed spaces as special cases of topological spaces. Algebraic structures equipped with topology: topological semigroups, topological groups, topological rings, topological algebras. Separation axioms. Hausdorff space and completely regular space. Compact and locally compact spaces. Connected and locally connected spaces.

Learning outcomes in the course

Upon completing the course the student:

- is familiar with the main concepts of topology;

- is able to use the concepts of topology in order to check the continuity of maps;

- knows the main classes of topological spaces and their properties.

- is familiar with the main concepts of topology;

- is able to use the concepts of topology in order to check the continuity of maps;

- knows the main classes of topological spaces and their properties.

Teacher

prof Mart Abel

Prerequisite course 1

Study programmes containing that course