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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
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Metric spaces and topology

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Code Completion Credits Range Language
D01MET_EN ZK 2P English
Garant předmětu:
Ondřej Zindulka
Lecturer:
Ondřej Zindulka
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

Topology and metric in the plane and Euclidean spaces; convergence, continuous functions and mappings. Metric spaces. Topology of metric spaces, convergence, continuous functions and mappings, Urysohn Lemma, Tietze Theorem. Complete metric spaces, Banach Fixed Point Lemma. Compact metric spaces. Compactness in Euclidean spaces. Lipschitz and Holder functions. Topology on a set. Open and closed sets, closure, boundary. Urysohn Lemma, Tietze Theorem.

Cartesian products, projections. Connected and totally disconnected spaces. Compactness. Tychonoff Theorem for finitely many spaces. Arzelá-Acoli Theorem. Stone-Weierstrass Theorem.

Requirements:
Syllabus of lectures:
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Note:
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
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The course is a part of the following study plans:
Data valid to 2024-05-22
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