A First Course in Topology

2014-05-21
A First Course in Topology

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  • Author: Robert A Conover
  • Publisher: Courier Corporation
  • ISBN: 0486780015
  • Category : Mathematics
  • Languages : en
  • Pages : 276

Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

A First Course in Topology

2006
A First Course in Topology

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  • Author: John McCleary
  • Publisher: American Mathematical Soc.
  • ISBN: 0821838849
  • Category : Mathematics
  • Languages : en
  • Pages : 226

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time.The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

A First Course in Geometric Topology and Differential Geometry

2011-06-27
A First Course in Geometric Topology and Differential Geometry

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  • Author: Ethan D. Bloch
  • Publisher: Springer Science & Business Media
  • ISBN: 0817681221
  • Category : Mathematics
  • Languages : en
  • Pages : 433

The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.

A First Course in Algebraic Topology

1980-09-25
A First Course in Algebraic Topology

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  • Author: Czes Kosniowski
  • Publisher: Cambridge University Press
  • ISBN: 9780521231954
  • Category : Mathematics
  • Languages : en
  • Pages : 284

This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.

Algebraic Topology

2013-12-01
Algebraic Topology

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  • Author: William Fulton
  • Publisher: Springer Science & Business Media
  • ISBN: 1461241804
  • Category : Mathematics
  • Languages : en
  • Pages : 435

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

Algebraic Topology

2018-03-05
Algebraic Topology

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  • Author: Marvin J. Greenberg
  • Publisher: CRC Press
  • ISBN: 0429982038
  • Category : Mathematics
  • Languages : en
  • Pages : 253

Great first book on algebraic topology. Introduces (co)homology through singular theory.

Introduction to Topology

2013-04-22
Introduction to Topology

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  • Author: Theodore W. Gamelin
  • Publisher: Courier Corporation
  • ISBN: 0486320189
  • Category : Mathematics
  • Languages : en
  • Pages : 258

This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Elementary Topology

Elementary Topology

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  • Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821886250
  • Category : Mathematics
  • Languages : en
  • Pages : 432

This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

A Course in Point Set Topology

2013-11-04
A Course in Point Set Topology

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  • Author: John B. Conway
  • Publisher: Springer Science & Business Media
  • ISBN: 3319023683
  • Category : Mathematics
  • Languages : en
  • Pages : 154

This textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.

A First Course in Algebraic Topology

2000
A First Course in Algebraic Topology

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  • Author: A. Lahiri
  • Publisher: Alpha Science Int'l Ltd.
  • ISBN: 9781842650035
  • Category : Mathematics
  • Languages : en
  • Pages : 132

This volume is an introductory text where the subject matter has been presented lucidly so as to help self study by the beginners. New definitions are followed by suitable illustrations and the proofs of the theorems are easily accessible to the readers. Sufficient number of examples have been incorporated to facilitate clear understanding of the concepts. The book starts with the basic notions of category, functors and homotopy of continuous mappings including relative homotopy. Fundamental groups of circles and torus have been treated along with the fundamental group of covering spaces. Simplexes and complexes are presented in detail and two homology theories-simplicial homology and singular homology have been considered along with calculations of some homology groups.