Quasi-Uniform Spaces

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 completenessand 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 studyQuasi-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. Language: English