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Bitopological spaces. (English) Zbl 0986.54040
J. Math. Sci., New York 98, No. 5, 509-616 (2000); translation from Zap.Nauchn. Semin. POMI 242, 7-216 (1997).
The present paper is a nice, almost complete, survey on the theory of bitopological spaces and its applications. The author is guided by two purposes: first to present some of his own results in the area and second to offer basic ideas, methods and problems both in the classical theory of bitopological spaces (in the sense of Kelly) and in the general theory of bitopological spaces as a part of the theory of spaces of topological type. The classical theory is described rather schematically in Chapter I, except the theory of extensions of topological and bitopological spaces and the theory of completion of uniform spaces which is presented thoroughly.
The main focus of the paper is in Chapter II, where notions, methods and results are presented with a lot of details and they have no analogues in the classical theory.
In chapters III and IV one can find some interesting applications of bitopological spaces, such as foundations of the theory of bitopological manifolds and bitopological groups, respectively.
It is worth mentioning that the author supports the whole theory of bitopological spaces with a lot of interesting examples, some of which are of fundamental importance.
MSC:
54E55 Bitopologies
54-02 Research exposition (monographs, survey articles) pertaining to general topology
Software:
Maple
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References:
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