Quasi-uniform spaces
著者
書誌事項
Quasi-uniform spaces
(Lecture notes in pure and applied mathematics, v. 77)
M. Dekker, c1982
- pbk.
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注記
Bibliography: p. 195-205
Includes index
内容説明・目次
内容説明
Since quasi-uniform spaces were defined in 1948, a diverse and widely dispersed literatureconcerning them has emerged. In Quasi-Uniform Spaces, the authors present a comprehensivestudy of these structures, together with the theory of quasi-proximities. In additionto new results unavailable elsewhere, the volume unites fundamental materialheretofore scattered throughout the literature.Quasi-Uniform Spaces shows by example that these structures provide a natural approachto the study of point-set topology. It is the only source for many results related to completeness,and a primary source for the study of both transitive and quasi-metric spaces.Included are H. Junnila's analogue of Tamano's theorem, J. Kofner's result showing thatevery GO space is transitive, and R. Fox's example of a non-quasi-metrizable r-space. Inaddition to numerous interesting problems mentioned throughout the text , 22 formalresearch problems are featured. The book nurtures a radically different viewpoint oftopology , leading to new insights into purely topological problems.Since every topological space admits a quasi-uniformity, the study of quasi-uniformspaces can be seen as no less general than the study of topological spaces. For such study,Quasi-Uniform Spaces is a necessary, self-contained reference for both researchers andgraduate students of general topology . Information is made particularly accessible withthe inclusion of an extensive index and bibliography .
目次
1. Elementary Properties of Quasi-Uniformities and Quasi-Proximities 2. Approximations of Symmetry 3. Completeness 4. Topological Ordered Spaces 5. Covering Properties of Quasi-Uniform Spaces 6. Transitive Spaces 7. Quasi-Metrizable Spaces
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