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Metric Space Topology: Examples, Exercises And Solutions

Author: Wing-sum Cheung

Publisher: World Scientific

Published: 2023-10-18

Total Pages: 442

ISBN-13: 9811266999

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:

Introductory Topology

Author: Mohammed Hichem Mortad

Publisher: World Scientific

Published:

Total Pages:

ISBN-13: 9813146958

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The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions. In the second edition, some significant changes have been made, other than the additional exercises. There are also additional proofs (as exercises) of many results in the old section "What You Need To Know", which has been improved and renamed in the new edition as "Essential Background". Indeed, it has been considerably beefed up as it now includes more remarks and results for readers' convenience. The interesting sections "True or False" and "Tests" have remained as they were, apart from a very few changes.

Topology of Metric Spaces

Author: S. Kumaresan

Publisher: Alpha Science Int'l Ltd.

Published: 2005

Total Pages: 172

ISBN-13: 9781842652503

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"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.

Introductory Topology: Exercises And Solutions

Author: Mohammed Hichem Mortad

Publisher: World Scientific Publishing Company

Published: 2014-02-28

Total Pages: 261

ISBN-13: 9814583839

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The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.

Metric Spaces

Author: Mícheál O'Searcoid

Publisher: Springer Science & Business Media

Published: 2006-12-26

Total Pages: 318

ISBN-13: 1846286271

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The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.

Metric Spaces

Author: Satish Shirali

Publisher: Springer Science & Business Media

Published: 2006

Total Pages: 238

ISBN-13: 9781852339227

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One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily

Basic Topology

Author: Dan Edwin Christie

Publisher:

Published: 1976

Total Pages: 276

ISBN-13:

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Introduction to Metric and Topological Spaces

Author: Wilson Alexander Sutherland

Publisher: Oxford University Press

Published: 1975

Total Pages: 200

ISBN-13: 9780198531616

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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.

An Illustrated Introduction to Topology and Homotopy Solutions Manual for Part 1 Topology

Author: Sasho Kalajdzievski

Publisher: CRC Press

Published: 2020-08-13

Total Pages: 152

ISBN-13: 1000158160

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This solution manual accompanies the first part of the book An Illustrated Introduction toTopology and Homotopy by the same author. Except for a small number of exercises inthe first few sections, we provide solutions of the (228) odd-numbered problemsappearing in first part of the book (Topology). The primary targets of this manual are thestudents of topology. This set is not disjoint from the set of instructors of topologycourses, who may also find this manual useful as a source of examples, exam problems,etc.

Introduction to Metric and Topological Spaces

Author: Wilson A Sutherland

Publisher: Oxford University Press

Published: 2009-06-18

Total Pages: 219

ISBN-13: 0191568309

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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.