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Space structures, their theory and application. II. (Russian, English) Zbl 1080.54001
Zap. Nauchn. Semin. POMI 313, 5-130, 139 (2004); translation in J. Math. Sci., New York 133, No. 5, 1543-1598 (2006).
This is the second part of a book of the author about “spaces structures and their applications” dealing with (1) topologies on the set of subsets of a given set \(X\), (2) topologies on product sets \(X \times Y\) and (3) function spaces. The book consists of three parts:
I. P-topological structures (topologies on a set of subsets of a set \(X\)).
II. Product structures and function spaces organized as follows: §1 Topological structures of function spaces, §2 Topological structures on products, §3 Topological structures on products and function spaces, §4, §5 Applications.
III. Some applications of space structures: §1 Bitopological manifolds, §2 Infinitisimal structures on \(\mathbb R^n\), §3 P-topological manifolds, §4, §5 Bitopological groups and special constructions (like subgroups, factorgroups and products), §6 Topological and bitopological groups, §7 Finite bitopological groups, §8 P-topological groups.
At the beginning there is a long categorial introduction (19 pages).
The book does not contain neither a table of contents, a bibliography nor an index, which makes reading not easier.

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