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An elementary course of general topology, necessary for the study branch Mathematical Structures and suitable also for the study branch Mathematical Analysis. The course brings basic notions and theorems.
Last update: T_KMA (15.05.2003)
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R. Engelking, General Topology, PWN Warszawa 1977 J. L. Kelley, General Topology, D. Van Nostrand, New York 1957 (ruský překlad Obščaja Topologija, Nauka, Moskva 1968) E. Čech, Topological Spaces, Academia, Praha 1966 Last update: G_I (28.05.2004)
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1. General: Topological spaces, open and closed sets, continuous mappings. 2. Basic constructions: Projective and inductive generation. Subspace, sum, product, quotient. Embedding lemma 3. Axioms of separation: T0, T1, Hausdorff, regular, completely regular, normal spaces. Embedding into the product of intervals, Urysohn lemmma, Tietze theorem 4. Uniform spaces: uniform cover, uniformly continuous mappings, subspace, sum, product, toppology of uniform spaces, complete uniform spaces, completion, extensions of uniformly continuous mappings. 5. Compact spaces: Tychonoff theorem, Baire theorem, Stone-Weierstrass theorem, Cech-Stone compactification. 6. Topological groups: Basic properties, group uniformity, topological properties of subgroups. Last update: G_I (28.05.2004)
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