Completeness and Precompactness in Quasi-uniform Topological Spaces PDF Download
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Author: Daniel Sherman Yates
Publisher:
ISBN:
Category : Topology
Languages : en
Pages : 62
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Book Description
Author: Y.-C. Wong
Publisher: Springer
ISBN: 3540382682
Category : Mathematics
Languages : en
Pages : 169
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Book Description
Author: M. G. Murdeshwar
Publisher:
ISBN:
Category : Quasi-uniform spaces
Languages : en
Pages : 92
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Book Description
Author: Daniel Sherman Yates
Publisher:
ISBN:
Category : Topology
Languages : en
Pages : 62
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Book Description
Author: Fletcher
Publisher: Routledge
ISBN: 1351420283
Category : Mathematics
Languages : en
Pages : 240
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Book Description
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 .
Author: Hans Joachim Kowalsky
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 304
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Book Description
Author: Michael Hrušák
Publisher: Springer
ISBN: 3319916807
Category : Mathematics
Languages : en
Pages : 309
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Book Description
This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.
Author: Frdric Mynard
Publisher: American Mathematical Soc.
ISBN: 082184279X
Category : Mathematics
Languages : en
Pages : 395
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Book Description
The purpose of this collection is to guide the non-specialist through the basic theory of various generalizations of topology, starting with clear motivations for their introduction. Structures considered include closure spaces, convergence spaces, proximity spaces, quasi-uniform spaces, merotopic spaces, nearness and filter spaces, semi-uniform convergence spaces, and approach spaces. Each chapter is self-contained and accessible to the graduate student, and focuses on motivations to introduce the generalization of topologies considered, presenting examples where desirable properties are not present in the realm of topologies and the problem is remedied in the more general context. Then, enough material will be covered to prepare the reader for more advanced papers on the topic. While category theory is not the focus of the book, it is a convenient language to study these structures and, while kept as a tool rather than an object of study, will be used throughout the book. For this reason, the book contains an introductory chapter on categorical topology.
Author: John Warnock Carlson
Publisher:
ISBN:
Category : Completeness theorem
Languages : en
Pages : 114
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Book Description
"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.
Author: William F. Lindgren
Publisher:
ISBN:
Category : Proximity spaces
Languages : en
Pages : 66
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Book Description
Author: Taqdir Husain
Publisher: Vieweg+Teubner Verlag
ISBN: 3322962105
Category : Mathematics
Languages : en
Pages : 115
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Book Description
THE main purpose of writing this monograph is to give a picture of the progress made in recent years in understanding three of the deepest results of Functional Analysis-namely, the open-mapping and closed graph theorems, and the so-called Krein-~mulian theorem. In order to facilitate the reading of this book, some of the important notions and well-known results about topological and vector spaces have been collected in Chapter 1. The proofs of these results are omitted for the reason that they are easily available in any standard book on topology and vector spaces e.g. Bourbaki [2], Keiley [18], or Köthe [22]. The results of Chapter 2 are supposed to be weil known for a study of topological vector spaces as weil. Most of the definitions and notations of Chapter 2 are taken from Bourbaki's books [3] and [4] with some trimming and pruning here and there. Keeping the purpose of this book in mind, the presentation of the material is effected to give a quick resume of the results and the ideas very commonly used in this field, sacrificing the generality of some theorems for which one may consult other books, e.g. [3], [4], and [22]. From Chapter 3 onward, a detailed study of the open-mapping and closed-graph theorems as weil as the Krein-~mulian theorem has been carried out. For the arrangement of the contents of Chapters 3 to 7, see the Historical Notes (Chapter 8).
