Topology Of Metric Spaces PDF Download
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| Author | : S. Kumaresan |
| Publisher | : Alpha Science Int'l Ltd. |
| Total Pages | : 172 |
| Release | : 2005 |
| Genre | : Computers |
| ISBN | : 9781842652503 |
Download Topology of Metric Spaces Book in PDF, ePub and Kindle
"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.
| Author | : Wilson A Sutherland |
| Publisher | : Oxford University Press |
| Total Pages | : 219 |
| Release | : 2009-06-18 |
| Genre | : Mathematics |
| ISBN | : 0191568309 |
Download Introduction to Metric and Topological Spaces Book in PDF, ePub and Kindle
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
| Author | : Robert B. Ash |
| Publisher | : Courier Corporation |
| Total Pages | : 216 |
| Release | : 2014-07-28 |
| Genre | : Mathematics |
| ISBN | : 0486151492 |
Download Real Variables with Basic Metric Space Topology Book in PDF, ePub and Kindle
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
| Author | : Avishek Adhikari |
| Publisher | : Springer Nature |
| Total Pages | : 523 |
| Release | : 2022-07-04 |
| Genre | : Mathematics |
| ISBN | : 9811665095 |
Download Basic Topology 1 Book in PDF, ePub and Kindle
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone–Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand–Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the concepts leading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
| Author | : Gerard Buskes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 321 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461206650 |
Download Topological Spaces Book in PDF, ePub and Kindle
gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.
| Author | : Wilson Alexander Sutherland |
| Publisher | : Oxford University Press |
| Total Pages | : 200 |
| Release | : 1975 |
| Genre | : Mathematics |
| ISBN | : 9780198531616 |
Download Introduction to Metric and Topological Spaces Book in PDF, ePub and Kindle
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This book introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces. The book is aimed primarily at the second-year mathematics student, and numerous exercises are included.
| Author | : Satish Shirali |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9781852339227 |
Download Metric Spaces Book in PDF, ePub and Kindle
One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
| Author | : Irving Kaplansky |
| Publisher | : American Mathematical Society |
| Total Pages | : 140 |
| Release | : 2020-09-10 |
| Genre | : Mathematics |
| ISBN | : 1470463849 |
Download Set Theory and Metric Spaces Book in PDF, ePub and Kindle
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 | : Wing-sum Cheung |
| Publisher | : World Scientific |
| Total Pages | : 442 |
| Release | : 2023-10-18 |
| Genre | : Mathematics |
| ISBN | : 9811266999 |
Download Metric Space Topology: Examples, Exercises And Solutions Book in PDF, ePub and Kindle
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 | : Wilson A Sutherland |
| Publisher | : Oxford University Press |
| Total Pages | : 219 |
| Release | : 2009-06-18 |
| Genre | : Mathematics |
| ISBN | : 0199563071 |
Download Introduction to Metric and Topological Spaces Book in PDF, ePub and Kindle
This fully updated new edition of Wilson Sutherland's classic text, Introduction to Metric and Topological Spaces, establishes the language of metric and topological spaces with continuity as the motivating concept, before developing its discussion to cover compactness, connectedness, and completeness.
