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 Zap. Nauchn. Sem. POMI, 1997, Volume 242, Pages 7–216 (Mi znsl486)

Bitopological spaces

A. A. Ivanov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The paper is, in essence, a monograph devoted to the theory of bitopological spaces and its applications. Not exhausting the entire subject, it reflects basic ideas and methods of the theory. The Introduction gives an idea of the origins of the basic notions, contents, methods, and problems both of the classical (in the spirit of Kelly) and of the general theory of bitopological spaces. The classical theory is described rather schematically in Chapter I, only the theory of extensions of topological and bitopological spaces and the theory of completion of uniform spaces are presented in more detail. The main focus is on the general theory of bitopological spaces (Chapter II). Notions, methods, and results presented here have no analogues in the classical theory. As applications, foundations of the theory of bitopological manifolds, in particular, bitopologically represented piecewise linear manifolds (Chapter III), and the foundations of the theory of bitopological groups are presented (Chapter IV).

Full text: PDF file (1160 kB)

English version:
Journal of Mathematical Sciences (New York), 2000, 98:5, 509–616

Bibliographic databases:

UDC: 515.122.4

Citation: A. A. Ivanov, “Bitopological spaces”, Bitopological space. Investigations in topology. Part 9, Zap. Nauchn. Sem. POMI, 242, POMI, St. Petersburg, 1997, 7–216; J. Math. Sci. (New York), 98:5 (2000), 509–616

Citation in format AMSBIB
\Bibitem{Iva97} \by A.~A.~Ivanov \paper Bitopological spaces \inbook Bitopological space. Investigations in topology. Part~9 \serial Zap. Nauchn. Sem. POMI \yr 1997 \vol 242 \pages 7--216 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl486} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1706129} \zmath{https://zbmath.org/?q=an:0986.54040} \transl \jour J. Math. Sci. (New York) \yr 2000 \vol 98 \issue 5 \pages 509--616 \crossref{https://doi.org/10.1007/BF02355742}