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| BITOPOLOGICAL SPACES: THEORY, RELATIONS WITH GENERALIZED ALGEBRAIC STRUCTURES AND APPLICATIONS, 199
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By
Badri Dvalishvili, B.P. Dvalishvili, Tbilisi, Georgia
Included in series
North-Holland Mathematics Studies, 199
Description
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"
Audience
Professional mathematicians and mathematics students
Contents
Preface
Chapter 0 Preliminaries
Chapter I Different Families of Sets in Bitopological Spaces
Chapter II Different Relations between Two
Topologies on a Set and Bitopological Insertions
Chapter III Dimension of Bitopological Spaces
Chapter IV Baire-Like Properties of Bitopological
Spaces
Chapter V Dynamics of Bitopological Relations, Baire-Like Properties and Dimensions
Chapter VI Generalized Boolean Algebras and
Related Problems. Representation Theorems
Chapter VII Applications of Bitopologies
Bibliography
List of Special Symbols and Notations
Index
| Bibliographic details |
Hardbound, 422 pages, publication date: JAN-2005
ISBN-13: 978-0-444-51793-7
ISBN-10: 0-444-51793-6
Imprint: NORTH-HOLLAND
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| Price and Ordering |
Price:
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GBP 126.99
EUR 149.95
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Last update: 3 Oct 2009
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