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Function Spaces with Uniform, Fine and Graph Topologies

2018-04-21 Mathematics
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Release : 2018-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 543/5 ( reviews)

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Book Synopsis Function Spaces with Uniform, Fine and Graph Topologies by : Robert A. McCoy

Download or read book Function Spaces with Uniform, Fine and Graph Topologies written by Robert A. McCoy. This book was released on 2018-04-21. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.

Recent Progress in Function Spaces

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Recent Progress in Function Spaces by : Giuseppe Di Maio

Download or read book Recent Progress in Function Spaces written by Giuseppe Di Maio. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt:

Uniform Spaces

1964-12-31 Mathematics
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Release : 1964-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 121/5 ( reviews)

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Book Synopsis Uniform Spaces by : John Rolfe Isbell

Download or read book Uniform Spaces written by John Rolfe Isbell. This book was released on 1964-12-31. 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.

Metric Spaces And Related Analysis

2023-10-16 Mathematics
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Release : 2023-10-16
Genre : Mathematics
Kind : eBook
Book Rating : 938/5 ( reviews)

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Book Synopsis Metric Spaces And Related Analysis by : Subiman Kundu

Download or read book Metric Spaces And Related Analysis written by Subiman Kundu. This book was released on 2023-10-16. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the comprehensive study of one of the foundational topics in Mathematics, known as Metric Spaces. The book delivers the concepts in an appropriate and concise manner, at the same time rich in illustrations and exercise problems. Special focus has been laid on important theorems like Baire's Category theorem, Heine-Borel theorem, Ascoli-Arzela Theorem, etc, which play a crucial role in the study of metric spaces.The additional chapter on Cofinal completeness, UC spaces and finite chainability makes the text unique of its kind. This helps the students in: Readers will also find brief discussions on various subtleties of continuity like subcontinuity, upper semi-continuity, lower semi-continuity, etc. The interested readers will be motivated to explore the special classes of functions between metric spaces to further extent.Consequently, the book becomes a complete package: it makes the foundational pillars strong and develops the interest of students to pursue research in metric spaces. The book is useful for third and fourth year undergraduate students and it is also helpful for graduate students and researchers.

Topological Properties of Spaces of Continuous Functions

2006-12-08 Mathematics
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Release : 2006-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 819/5 ( reviews)

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Book Synopsis Topological Properties of Spaces of Continuous Functions by : Robert A. McCoy

Download or read book Topological Properties of Spaces of Continuous Functions written by Robert A. McCoy. This book was released on 2006-12-08. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together into a general setting various techniques in the study of the topological properties of spaces of continuous functions. The two major classes of function space topologies studied are the set-open topologies and the uniform topologies. Where appropriate, the analogous theorems for the two major classes of topologies are studied together, so that a comparison can be made. A chapter on cardinal functions puts characterizations of a number of topological properties of function spaces into a more general setting: some of these results are new, others are generalizations of known theorems. Excercises are included at the end of each chapter, covering other kinds of function space topologies. Thus the book should be appropriate for use in a classroom setting as well as for functional analysis and general topology. The only background needed is some basic knowledge of general topology.

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