| Edition |
1st ed. |
| Description |
1 online resource (xiii, 415 pages) |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
North-Holland mathematics studies ; 199 |
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North-Holland mathematics studies ; 199.
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| Summary |
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 |
| 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. |
| Bibliography |
Includes bibliographical references (pages 321-332) and index. |
| Note |
Print version record. |
| Subject |
Topological spaces.
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Topology.
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Metric spaces.
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Espaces topologiques.
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Topologie.
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Espaces métriques.
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MATHEMATICS -- Topology.
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Metric spaces
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Topological spaces
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Topology
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| Other Form: |
Print version: Dvalishvili, B.P. Bitopological spaces. 1st ed. Amsterdam ; Boston : Elsevier, ©2005 0444517936 9780444517937 (OCoLC)57506124 |
| ISBN |
9780444517937 |
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0444517936 |
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0080459463 (electronic bk.) |
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9780080459462 (electronic bk.) |
| Standard No. |
AU@ 000048131005 |
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AU@ 000062569863 |
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CHNEW 001005604 |
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DEBBG BV036962238 |
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DEBBG BV039830107 |
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DEBBG BV042317256 |
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DEBSZ 276340302 |
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DEBSZ 48235156X |
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NZ1 12434493 |
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