Topology

Author: James R. Munkres
Publisher: Prentice Hall
ISBN:
Format: PDF
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This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

Algebraic Topology

Author: Edwin H. Spanier
Publisher: Springer Science & Business Media
ISBN: 1468493221
Format: PDF, ePub, Mobi
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This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Topology

Author:
Publisher: Academic Press
ISBN: 9780080873312
Format: PDF, Mobi
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Topology

Fuzzy Topology

Author: N. Palaniappan
Publisher: CRC Press
ISBN: 9780849324161
Format: PDF
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In recent years, many concepts in mathematics, engineering, computer science, and many other disciplines have been in a sense redefined to incorporate the notion of fuzziness. Designed for graduate students and research scholars, Fuzzy Topology imparts the concepts and recent developments related to the various properties of fuzzy topology. The author first addresses fundamental problems, such as the idea of a fuzzy point and its neighborhood structure and the theory of convergence. He then studies the connection between fuzzy topological spaces and topological spaces and introduces fuzzy continuity and product induced spaces. Chapter Three examines fuzzy nets, fuzzy upper and lower limits, and fuzzy convergence and is followed by a study of fuzzy metric spaces. The treatment then introduces the concept of fuzzy compactness before moving to initial and final topologies and the fuzzy Tychnoff theorem. The final sections of the book cover connectedness, complements, separation axioms, and uniform spaces.

Elementary Topology

Author: Michael C. Gemignani
Publisher: Courier Corporation
ISBN: 9780486665221
Format: PDF, Docs
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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.

Algebraic and Differential Topology

Author: R. V. Gamkrelidze
Publisher: CRC Press
ISBN: 9782881240355
Format: PDF, ePub, Docs
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Algebraic and Differential Topology presents in a clear, concise, and detailed manner the fundamentals of homology theory. It first defines the concept of a complex and its Betti groups, then discusses the topolgoical invariance of a Betti group. The book next presents various applications of homology theory, such as mapping of polyhedrons onto other polyhedrons as well as onto themselves. The third volume in L.S. Pontryagin's Selected Works, this book provides as many insights into algebraic topology for today's mathematician as it did when the author was making his initial endeavors into this field.

Topology

Author: John Gilbert Hocking
Publisher: Courier Corporation
ISBN: 0486656764
Format: PDF
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Designed as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.

Algebraic Topology

Author: Allen Hatcher
Publisher: Cambridge University Press
ISBN: 9780521795401
Format: PDF, ePub, Docs
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An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Topology

Author: Donald W. Kahn
Publisher: Courier Corporation
ISBN: 9780486686097
Format: PDF, ePub
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Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.