Introduction to Topology and Geometry by Saul Stahl; Catherine Stenson 2013An easily accessible introduction to over threecenturies of innovations in geometry Praise for the First Edition ". . . a welcome alternative to compartmentalizedtreatments bound to the old thinking. This clearly written,well-illustrated book supplies sufficient background to beself-contained." --CHOICE This fully revised new edition offers the most comprehensivecoverage of modern geometry currently available at an introductorylevel. The book strikes a welcome balance between academic rigorand accessibility, providing a complete and cohesive picture of thescience with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction toTopology and Geometry, Second Edition discusses introductorytopology, algebraic topology, knot theory, the geometry ofsurfaces, Riemann geometries, fundamental groups, and differentialgeometry, which opens the doors to a wealth of applications. Withits logical, yet flexible, organization, the SecondEdition: * Explores historical notes interspersed throughout theexposition to provide readers with a feel for how the mathematicaldisciplines and theorems came into being * Provides exercises ranging from routine to challenging,allowing readers at varying levels of study to master the conceptsand methods * Bridges seemingly disparate topics by creating thoughtfuland logical connections * Contains coverage on the elements of polytope theory, whichacquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is anexcellent introductory text for topology and geometry courses atthe upper-undergraduate level. In addition, the book serves as anideal reference for professionals interested in gaining a deeperunderstanding of the topic.
ISBN: 9781118108109
Publication Date: 2013-03-11
Introduction to Topology by Min Yan; Higher Education Press Ltd. Higher Education Press Ltd. Comp. (Contribution by) 2016The aim of the book is to give a broad introduction of topology to undergraduate students. It covers the most important and useful parts of the point-set as well as the combinatorial topology. The development of the material is from simple to complex, concrete to abstract, and appeals to the intuition of readers. Attention is also paid to how topology is actually used in the other fields of mathematics. Over 150 illustrations, 160 examples and 600 exercises will help readers to practice and fully understand the subject. Contents: Set and Map Metric Space Graph Topology Topological Concepts Complex Topological Properties Surface Topics in Point Set Topology Index
ISBN: 9783110378153
Publication Date: 2016-02-22
Topology by D. Chatterjee 2007About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the realm of differentiable manifold and fibre bundles. It should be usefull for mathematicians as well as Physicists desiring to acquire overall knowledge of algebraic topology and its tools. Contents: PART I- Sets, Relations and Functions Topology of R and R2 Metric Space Topological Spaces Separation Axioms Compactness Connectedness PART II - Algebraic Preliminaries Homotopy Theory Compact Open Topology Higher Homotopy Groups Surfaces, Manifolds and CW-complexes Simplicial Homology Theory Singular Homology Theory Manifold Analysis Fibre Bundles