Elementary Topology
Title | Elementary Topology PDF eBook |
Author | O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov |
Publisher | American Mathematical Soc. |
Total Pages | 432 |
Release | |
Genre | Mathematics |
ISBN | 9780821886250 |
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.
Elementary Topology
Title | Elementary Topology PDF eBook |
Author | Michael C. Gemignani |
Publisher | Courier Corporation |
Total Pages | 292 |
Release | 1990-01-01 |
Genre | Mathematics |
ISBN | 9780486665221 |
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.
Elementary Concepts of Topology
Title | Elementary Concepts of Topology PDF eBook |
Author | Paul Alexandroff |
Publisher | Courier Corporation |
Total Pages | 68 |
Release | 2012-08-13 |
Genre | Mathematics |
ISBN | 0486155064 |
Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Intuitive Concepts in Elementary Topology
Title | Intuitive Concepts in Elementary Topology PDF eBook |
Author | B.H. Arnold |
Publisher | Courier Corporation |
Total Pages | 192 |
Release | 2015-02-23 |
Genre | Mathematics |
ISBN | 0486275760 |
Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.
Elementary Applied Topology
Title | Elementary Applied Topology PDF eBook |
Author | Robert W. Ghrist |
Publisher | Createspace Independent Publishing Platform |
Total Pages | 0 |
Release | 2014 |
Genre | Mathematics |
ISBN | 9781502880857 |
This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in the context of applications drawn from the biological, economic, engineering, physical, and statistical sciences.
Elementary Topology And Applications (Second Edition)
Title | Elementary Topology And Applications (Second Edition) PDF eBook |
Author | Carlos R Borges |
Publisher | World Scientific |
Total Pages | 174 |
Release | 2021-07-21 |
Genre | Mathematics |
ISBN | 9811237441 |
The textbook is a very good start into the mathematical field of topology. A variety of topological concepts with some elementary applications are introduced. It is organized in such a way that the reader gets to significant applications quickly.This revised version corrects the many discrepancies in the earlier edition. The emphasis is on the geometric understanding and the use of new concepts, indicating that topology is really the language of modern mathematics.
Lecture Notes on Elementary Topology and Geometry
Title | Lecture Notes on Elementary Topology and Geometry PDF eBook |
Author | I.M. Singer |
Publisher | Springer |
Total Pages | 240 |
Release | 2015-05-28 |
Genre | Mathematics |
ISBN | 1461573475 |
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.