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Course Title

Differential Geometry and Topology

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Year of study,

speciality 

2, Speciality – “Mathematics”, focus area: “scientific and pedagogical activity”

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Semester of study

3

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Credit points

3

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Name of the lecturer, scientific degree, occupation

Hleb O. Kukrak, PhD in Mathematics

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Goals of studying

Studying series of properties of metric and topological spaces and their connections with objects which studying in others courses (Analytical Geometry, Mathematical Analysis, Functional Analysis).

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Prerequisites

Introduction to Mathematics, Analytical Geometry, Mathematical Analysis.

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Contents

Metric and topological spaces and their geometry. Continuous maps and homeomorfisms. Connected spaces. Compact spaces. Complete metric spaces and compact metric spaces. Bases and dense sets in the topological spaces. Separabale spaces. The construction of the product of topological spaces. Factor-spaces of topological spaces.

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Recommended literature

1. Kononov S.G., Prasolov A.V., Timochovich V.L.,Tralle A.E., Fedenko A.S. Topology – Minsk: Vysheishaya Shcola,1990 (in Russian).
2. Aleksandrov P.S. Introduction in the set theory and general topology. – Moscow: Nauka, 1977 (in Russian).

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Teaching methodology

Comparative, problem, interactive-heuristic and visual.

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Language of instruction  

Russian

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Requirements for study during the semester

– tests

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Examination methodology

Examination