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Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications, Volume 199 (Hardcover, New)
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Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications, Volume 199 (Hardcover, New)
Series: North-Holland Mathematics Studies
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This monograph is the first and an initial introduction to the
theory of bitopological spaces and its applications. In particular,
different families of subsets of bitopological spaces are
introduced and various relations between two topologies are
analyzed on one and the same set; the theory of dimension of
bitopological spaces and the theory of Baire bitopological spaces
are constructed, and various classes of mappings of bitopological
spaces are studied. The previously known results as well the
results obtained in this monograph are applied in analysis,
potential theory, general topology, and theory of ordered
topological spaces. Moreover, a high level of modern knowledge of
bitopological spaces theory has made it possible to introduce and
study algebra of new type, the corresponding representation of
which brings one to the special class of bitopological spaces.
It is beyond any doubt that in the nearest future the areas of
essential applications will be the theories of linear topological
spaces and topological groups, algebraic and differential
topologies, the homotopy theory, not to mention other fundamental
areas of modern mathematics such as geometry, mathematical logic,
the probability theory and many other areas, including those of
applied nature.
Key Features:
- First monograph is "Generalized Lattices"
* The first introduction to the theory of bitopological spaces and
its applications.
General
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