First Concepts of Topology

First Concepts of Topology
Author: William G. Chinn
Publisher: MAA
Total Pages: 170
Release: 1966
Genre: Mathematics
ISBN: 0883856182

Over 150 problems and solutions.

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.

A First Course in Topology

A First Course in Topology
Author: Robert A Conover
Publisher: Courier Corporation
Total Pages: 276
Release: 2014-05-21
Genre: Mathematics
ISBN: 0486780015

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 Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology
Author: Michael Henle
Publisher: Courier Corporation
Total Pages: 340
Release: 1994-01-01
Genre: Mathematics
ISBN: 9780486679662

Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

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.

Introduction to Topology

Introduction to Topology
Author: Crump W. Baker
Publisher:
Total Pages: 155
Release: 1997
Genre: Mathematics
ISBN: 9781575240084

The fundamental concepts of general topology are covered in this text whic can be used by students with only an elementary background in calculus. Chapters cover: sets; functions; topological spaces; subspaces; and homeomorphisms.

Introduction to Topology

Introduction to Topology
Author: Tej Bahadur Singh
Publisher: Springer
Total Pages: 458
Release: 2019-05-17
Genre: Mathematics
ISBN: 9811369542

Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad range of mathematical disciplines, while algebraic topology offers as a powerful tool for studying problems in geometry and numerous other areas of mathematics. This book presents the basic concepts of topology, including virtually all of the traditional topics in point-set topology, as well as elementary topics in algebraic topology such as fundamental groups and covering spaces. It also discusses topological groups and transformation groups. When combined with a working knowledge of analysis and algebra, this book offers a valuable resource for advanced undergraduate and beginning graduate students of mathematics specializing in algebraic topology and harmonic analysis.

An Introduction to Algebraic Topology

An Introduction to Algebraic Topology
Author: Andrew H. Wallace
Publisher: Courier Corporation
Total Pages: 212
Release: 2011-11-30
Genre: Mathematics
ISBN: 0486152952

This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

Basic Concepts of Algebraic Topology

Basic Concepts of Algebraic Topology
Author: F.H. Croom
Publisher: Springer Science & Business Media
Total Pages: 187
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468494759

This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.