Metric Space Topology Examples Exercises And Solutions

Author : Wing-sum Cheung
Publisher : World Scientific
Page : 442 pages
File Size : 51,6 Mb
Release : 2023-10-18
Category : Mathematics
ISBN : 9789811266997

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Metric Space Topology: Examples, Exercises And Solutions by Wing-sum Cheung Pdf

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 : Mohammed Hichem Mortad
Publisher : World Scientific Publishing Company
Page : 260 pages
File Size : 41,6 Mb
Release : 2014-02-28
Category : Mathematics
ISBN : 9789814583831

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Introductory Topology by Mohammed Hichem Mortad Pdf

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.

Author : Mohammed Hichem Mortad
Publisher : World Scientific
Page : 128 pages
File Size : 54,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789813146952

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Introductory Topology by Mohammed Hichem Mortad Pdf

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.

Author : Satish Shirali,Harkrishan Lal Vasudeva
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 46,5 Mb
Release : 2005-12-16
Category : Mathematics
ISBN : 9781846282447

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Metric Spaces by Satish Shirali,Harkrishan Lal Vasudeva Pdf

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

Author : Sasho Kalajdzievski,Derek Krepski,Damjan Kalajdzievski
Publisher : CRC Press
Page : 110 pages
File Size : 50,9 Mb
Release : 2020-08-13
Category : Mathematics
ISBN : 9781000115369

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An Illustrated Introduction to Topology and Homotopy Solutions Manual for Part 1 Topology by Sasho Kalajdzievski,Derek Krepski,Damjan Kalajdzievski Pdf

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.

Author : Sasho Kalajdzievski,Derek Krepski,Damjan Kalajdzievski
Publisher : CRC Press
Page : 152 pages
File Size : 46,6 Mb
Release : 2020-08-13
Category : Mathematics
ISBN : 9781000158168

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An Illustrated Introduction to Topology and Homotopy Solutions Manual for Part 1 Topology by Sasho Kalajdzievski,Derek Krepski,Damjan Kalajdzievski Pdf

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.

Author : Dan Edwin Christie
Publisher : Unknown
Page : 276 pages
File Size : 41,5 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015035226425

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Basic Topology by Dan Edwin Christie Pdf

Author : Mícheál O'Searcoid
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 46,6 Mb
Release : 2006-12-26
Category : Mathematics
ISBN : 9781846286278

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Metric Spaces by Mícheál O'Searcoid Pdf

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.

Author : Wilson Alexander Sutherland
Publisher : Oxford University Press
Page : 200 pages
File Size : 43,6 Mb
Release : 1975
Category : Mathematics
ISBN : 0198531613

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Introduction to Metric and Topological Spaces by Wilson Alexander Sutherland Pdf

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 : S. Kumaresan
Publisher : Alpha Science Int'l Ltd.
Page : 172 pages
File Size : 54,5 Mb
Release : 2005
Category : Computers
ISBN : 1842652508

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Topology of Metric Spaces by S. Kumaresan Pdf

"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 : B. Schweizer,A. Sklar
Publisher : Courier Corporation
Page : 354 pages
File Size : 43,6 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 9780486445144

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Probabilistic Metric Spaces by B. Schweizer,A. Sklar Pdf

This distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs. The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.

Author : Robert Magnus
Publisher : Springer Nature
Page : 258 pages
File Size : 42,8 Mb
Release : 2022-03-16
Category : Mathematics
ISBN : 9783030949464

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Metric Spaces by Robert Magnus Pdf

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material. The book covers the main topics of metric space theory that the student of analysis is likely to need. Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment of continuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties. Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them. A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur–Ulam theorem, Picard’s theorem on existence of solutions to ordinary differential equations, and space filling curves. This text will be useful to all undergraduate students of mathematics, especially those who require metric space concepts for topics such as multivariate analysis, differential equations, complex analysis, functional analysis, and topology. It includes a large number of exercises, varying from routine to challenging. The prerequisites are a first course in real analysis of one real variable, an acquaintance with set theory, and some experience with rigorous proofs.

Author : Aisling McCluskey,Brian McMaster
Publisher : OUP Oxford
Page : 176 pages
File Size : 50,6 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9780191006739

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Undergraduate Topology by Aisling McCluskey,Brian McMaster Pdf

This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp ideas precisely and to argue with straight and careful logic. Research and long experience in undergraduate mathematics education suggests that an optimal way to learn such a subject is to teach it to yourself, pro-actively, by guided reading of brief skeleton notes and by doing your own spadework to fill in the details and to flesh out the examples. This text will facilitate such an approach for those learners who opt to do it this way and for those instructors who would like to encourage this so-called 'Moore approach', even for a modest segment of the teaching term or for part of the class. In reality, most students simply do not have the combination of time, background and motivation needed to implement such a plan fully. The accessibility, flexibility and completeness of this text enable it to be used equally effectively for more conventional instructor-led courses. Critically, it furnishes a rich variety of exercises and examples, many of which have specimen solutions, through which to gain in confidence and competence.

Author : Satish Shirali,Harkrishan Lal Vasudeva
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 43,8 Mb
Release : 2006
Category : Mathematics
ISBN : 1852339225

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Metric Spaces by Satish Shirali,Harkrishan Lal Vasudeva Pdf

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

Author : Michael C. Gemignani
Publisher : Addison Wesley Publishing Company
Page : 296 pages
File Size : 46,5 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:49015000695222

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Elementary Topology by Michael C. Gemignani Pdf

Superb introduction to metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, other essentials. Numerous exercises, plus section on paracompactness and complete regularity. References. Includes 107 illustrations.