General Topology
space
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 2022/2023 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2022/2023 Spring 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.
Teacher
prof Mart Abel
space