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Elements of mathematics. General topology. Chapters 1-4. Transl. from the French. 2nd printing. (English) Zbl 0683.54003
Berlin etc.: Springer-Verlag. vii, 437 p. DM 108.00 (1989).
Summary: This book is a reprint of the 1966 edition. Starting from the definitions, it gives a thorough treatment of the basic (and often non- trivial) aspects of general topology. In chapter I, general topological notions are introduced (including filters). Hausdorff, regular, compact, locally compact spaces are studied, as well as proper mappings and connectedness properties. Chapter II deals with uniform structures, complete spaces and the relationship between compactness and completeness. Chapter III treats topological groups, transposing into a topological setting the main aspects of group theory. Chapter IV applies the previous notions to the construction and study of the field of real numbers: real-valued functions and semi-continuity properties are defined, infinite sums and products are studied, and the usual expansions of real numbers given.

MSC:
54-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology
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