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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).