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.
Author(s): B.P. Dvalishvili (Eds.)
Series: North-Holland Mathematics Studies 199
Publisher: Elsevier Science & Technology
Year: 2005
Language: English
Pages: 1-415
Content:
Preface
Pages ix-xii
Chapter 0 Preliminaries Original Research Article
Pages 1-15
Chapter I Different families of sets in bitopological spaces Original Research Article
Pages 16-62
Chapter II Different relations between two topologies on a set and bitopological insertions Original Research Article
Pages 63-96
Chapter III Dimension of Bitopological Spaces Original Research Article
Pages 97-127
Chapter IV Baire-Like properties of bitopological spaces Original Research Article
Pages 128-162
Chapter V Dynamics of bitopological relations, baire-like properties and dimensions Original Research Article
Pages 163-192
Chapter VI Generalized boolean algebras and related problems. Representation theorems Original Research Article
Pages 193-317
Chapter VII Applications of bitopologies Original Research Article
Pages 318-384
Bibliography
Pages 385-398
List of Special Symbols and Notations
Pages 399-405
Index
Pages 406-415