Elementary Topology And Applications (Second Edition)

Elementary Topology And Applications (Second Edition)
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.

Elementary Topology and Applications

Elementary Topology and Applications
Author: Carlos R. Borges
Publisher: World Scientific
Total Pages: 224
Release: 2000
Genre: Mathematics
ISBN: 9789810242404

Based on the theme that topology is really the universal language of modern mathematics, Borges (mathematics, U. of California-Davis) introduces it to students who have a good grasp of fundamentals of logic, set theory, elementary analysis, and group theory. He gets rapidly to applications. His goal is to prepare students for further study in mathematics. He does not include bibliographic references. Annotation copyrighted by Book News, Inc., Portland, OR

Elementary Concepts of Topology

Elementary Concepts of Topology
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.

Elementary Topology

Elementary Topology
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.

Introduction to Topology

Introduction to Topology
Author: Theodore W. Gamelin
Publisher: Courier Corporation
Total Pages: 258
Release: 2013-04-22
Genre: Mathematics
ISBN: 0486320189

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.

Lecture Notes on Elementary Topology and Geometry

Lecture Notes on Elementary Topology and Geometry
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.

Elementary Applied Topology

Elementary Applied Topology
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.

Introduction to Topology

Introduction to Topology
Author: Bert Mendelson
Publisher: Courier Corporation
Total Pages: 226
Release: 2012-04-26
Genre: Mathematics
ISBN: 0486135098

Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Topology with Applications

Topology with Applications
Author: Somashekhar A. Naimpally
Publisher: World Scientific
Total Pages: 294
Release: 2013
Genre: Mathematics
ISBN: 9814407666

The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.