Download or read book Quasi Uniform Spaces written by Peter Fletcher and published by Routledge. This book was released on 2018-04-27 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 .

Download or read book Quasi uniform Topological Spaces written by M. G. Murdeshwar and published by . This book was released on 1966 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Convergence Precompactness and Symmetry in Quasi uniform Spaces written by Hans Paul Künzi and published by . This book was released on 1991 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quasi uniform Spaces written by p;lindgren fletcher (wf) and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Uniform Spaces written by I. M. James and published by Cambridge University Press. This book was released on 1990-05-03 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.

Download or read book Non Hausdorff Topology and Domain Theory written by Jean Goubault-Larrecq and published by Cambridge University Press. This book was released on 2013-03-28 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.

Download or read book Uniform Spaces written by John Rolfe Isbell and published by American Mathematical Soc.. This book was released on 1964-12-31 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniform spaces play the same role for uniform continuity as topological spaces for continuity. The theory was created in 1936 by A. Weil, whose original axiomatization was soon followed by those of Bourbaki and Tukey; in this book use is made chiefly of Tukey's system, based on uniform coverings. The organization of the book as a whole depends on the Eilenberg-MacLane notions of category, functor and naturality, in the spirit of Klein's Erlanger Program but with greater reach. The preface gives a concise history of the subject since 1936 and a foreword outlines the category theory of Eilenberg and MacLane. The chapters cover fundamental concepts and constructions; function spaces; mappings into polyhedra; dimension (1) and (2); compactifications and locally fine spaces. Most of the chapters are followed by exercises, occasional unsolved problems, and a major unsolved problem; the famous outstanding problem of characterizing the Euclidean plane is discussed in an appendix. There is a good index and a copious bibliography intended not to itemize sources but to guide further reading.

Download or read book The Scale of a Quasi Uniform Space written by Olivier Olela Otafudu and published by LAP Lambert Academic Publishing. This book was released on 2010-12 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: We continue our investigations of the scale of a quasi-uniform space, which we had started in an earlier article. We distinguish between the left-sided scale and the two-sided scale of a quasi-uniform space. While the behavior of the two-sided scale of a quasi-uniform space X shows similarities with the usual hyperspace of X equipped with its Hausdorff quasi-uniformity, the left-handed scale generalizes the quasi-uniform multifunction space of X into itself.For instance the two-sided scale of any totally bounded quasi-uniform space X is totally bounded, while total boundedness of the left-sided scale of a quasi-uniform space X implies that X is finite or indiscrete. Either construction of the scale is based on the idea of the prefilter space of a quasi-uniform space. Prefilter spaces of quasi-uniform spaces are shown to be bicomplete. It follows that both the left-sided and the two-sided scale of a quasi-uniform space are bicomplete. Indeed these scales can be used to construct the bicompletion of the T0-reflection of the Hausdorff quasi-uniformity of a quasi-uniform space.

Download or read book Uniformization of Quasi uniform Spaces written by Ivan L. Reilly and published by . This book was released on 1977 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Some Results on Quasi uniform Spaces written by Karen Sylvia Carter and published by . This book was released on 1973 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transitive Quasi uniform Spaces written by Michael Norman Halpin and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Local Properties of Transitive Quasi uniform Spaces written by Massood Seyedin and published by . This book was released on 1972 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Large completions of quasi uniform spaces written by Hermann Render and published by . This book was released on 1993 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Completeness and Related Topics in a Quasi uniform Space written by John Warnock Carlson and published by . This book was released on 1970 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Completions and a strong completion of a quasi-uniform space are constructed and examined. It is shown that the trivial completion of a T0 space is T0 . Examples are given to show that a T1 space need not have a T1 strong completion and a T2 space need not have a T2 completion. The nontrivial completion constructed is shown to be T1 if the space is T1 and the quasi-uniform structure is the Pervin structure. It is shown that a space can be uniformizable and admit a strongly complete quasi-uniform structure and not admit a complete uniform structure. Several counter-examples are provided concerning properties which hold in a uniform space but do not hold in a quasi-uniform space. It is shown that if each member of a quasi-uniform structure is a neighborhood of the diagonal then the topology is uniformizable"--Abstract, leaf ii.

Download or read book Topology and Its Applications written by Sergeĭ Petrovich Novikov and published by American Mathematical Soc.. This book was released on 1993 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of an international topology conference - this book covrs various aspects of general algebraic, and low-dimensional topology.

Download or read book Dense Subspaces of Quasi uniform Spaces written by Adrian Lüthy and published by . This book was released on 1991 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Categorical Aspects of the Theory of Quasi uniform Spaces written by G. C. L. Brümmer and published by . This book was released on 1997 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: