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Author: Subiman Kundu
Publisher: World Scientific
ISBN: 9811272670
Category : Mathematics
Languages : en
Pages : 151
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Book Description
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
Author: Subiman Kundu
Publisher: World Scientific
ISBN: 9811272670
Category : Mathematics
Languages : en
Pages : 151
Get Book Here
Book Description
The monograph targets a huge variety of characterizations of cofinally complete metric spaces. These spaces are studied in terms of several properties of some classes of functions between metric spaces that are stronger than the continuous functions such as Cauchy-regular, uniformly continuous, strongly uniformly continuous, and various Lipschitz-type functions. There is one chapter that is dedicated to studying cofinally complete metric spaces in terms of hyperspace and function space topologies. Along with that, various characterizations are studied in terms of geometric functionals, sequences, Cantor-type conditions, etc. The study of such spaces is interesting as well as it has nice connections with various other branches of mathematics such as convex analysis, optimization theory, fixed point theory, functional analysis and approximation theory. But until now, there has been no textbook or research monograph which presents the entire theory of these spaces in a comprehensive way. The study of the aforesaid spaces and their variants is still a vibrant area of research, and many prominent researchers are working in this area.The book is targeted at researchers as well as graduate students interested in real functions, analysis on metric spaces, topology, and the aforementioned. Since the monograph often discusses various properties of Lipschitz-type functions, it would be of interest to people interested in PDEs as well.
Author: Subiman Kundu
Publisher: World Scientific
ISBN: 9811278938
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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.
Author: Satish Shirali
Publisher: Springer Science & Business Media
ISBN: 9781852339227
Category : Mathematics
Languages : en
Pages : 238
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Book Description
One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Author: Wing-sum Cheung
Publisher: World Scientific
ISBN: 9811266999
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially conducive to the understanding of the materials. This serves to give an insightful view of the intricate problems, as well as a clue or a direction to formulate rigorous arguments.The learning outcomes include:
Author: Victor Bryant
Publisher: Cambridge University Press
ISBN: 9780521318976
Category : Mathematics
Languages : en
Pages : 116
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Book Description
An introduction to metric spaces for those interested in the applications as well as theory.
Author: Irving Kaplansky
Publisher: American Mathematical Soc.
ISBN: 0821826948
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This is a book that could profitably be read by many graduate students or by seniors in strong major programs ... has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. ... There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem ... The presentation of metric spaces before topological spaces ... should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. --Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. -- Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.
Author: Michael C. Gemignani
Publisher: Courier Corporation
ISBN: 9780486665221
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.
Author: Manabendra Nath Mukherjee
Publisher: Academic Publishers
ISBN: 9788189781989
Category : Metric spaces
Languages : en
Pages : 216
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Book Description
Author: E. T. Copson
Publisher: CUP Archive
ISBN: 9780521357326
Category : Mathematics
Languages : en
Pages : 156
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Book Description
Professor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.
Author: Pawan K. Jain
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842651704
Category : Mathematics
Languages : en
Pages : 178
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Book Description
Encouraged by the response to the first edition the authors have thoroughly revised Metric Spaces by incorporating suggestions received from the readers.
