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Space structures: theory and applications. (English. Russian original) Zbl 1072.54002
J. Math. Sci., New York 125, No. 1, 1-97 (2005); translation from Zap. Nauchn. Semin. POMI 287, 5-226 (2002).
This is the translation by the author himself of the first part of a book “Space Structures: Theory and Applications”. Unlike other books on point set theory the material is not developed starting from a general concept of a topological space, but by endowing a set with certain structures, a topology is only one possible choice. The chapters of the book are:
I Structures and categories; II Structures of metric type (dealing with metric spaces and metric structures not satisfying all axioms of a metric space); III Continuity structures (topological, weakly topological and quasi topological spaces); IV Extension structures; and two chapters dealing with bitopological spaces: V Classical bitopological structures; VI The general theory of bitopological spaces.
In Chapter V the author deals with sets carrying two different topologies, while in Chapter VI a bitopology is a topology in the product \(X \times X\) for a given set \(X\).

MSC:
54A05 Topological spaces and generalizations (closure spaces, etc.)
54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54E55 Bitopologies
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