Topology A Core Course

Description

Topology, as a subject, has become ubiquitous in almost every branch of Mathematics. It is now
a core course at the Masters or Honours level in almost every university. This book develops the
fundamental ideas and concepts of Topology, with an emphasis on topics and results that are
needed in modern Topology and its applications to other disciplines.

Salient Features :

The focus is on core concepts of the subject, and can be used as a starting point for learning
niche topics.
A variety of examples are given. And used repeatedly to explain every new concept introduced.
There are about 390 exercises scattered throughout the book. Hints and solutions are provided
for all exercises.
The exercises are of two types. Some within the chapter, to help motivate and understand the
concepts introduced. Some at the end of the chapter, to help review and consolidate.
Strategy and motivation for all proofs are given to enable diligent readers to work out details on
their own.
All concepts are developed keeping both students and teachers in mind. This book is an
excellent source for self-study. It lays a good foundation for more advanced topics. It has many
ideas, examples and exercises which may be of use to teachers teaching the subject.

About the Authors :

Vikram Aithal is a faculty at the Institute of Chemical Technology, Mumbai. He did his
Ph.D. at IIT Bombay after which he held post-doctoral, teaching and visiting positions
at various leading institutes in India and abroad. He has been associated with the
MTTS Programmes for several years.
S. Kumaresan is the first recipient of the Indo-Canadian Mathematics forum for
Excellence in Teaching and Research. He is also the first recipient of the INSA
Teaching Award for Mathematics. He did his Ph.D. at TIFR, Mumbai and then served
as a Professor at the University of Mumbai and the University of Hyderabad. He has
been a visiting Professor at many leading institutes both in India and abroad. He is
known for founding the Mathematics Training and Talent Search Programme. After
retirement, he continues to teach mathematics and spread the knowledge through
his very popular you tube channel.

The focus is on core concepts of the subject, and can be used as a starting point for learning
niche topics.
A variety of examples are given. And used repeatedly to explain every new concept introduced.
There are about 390 exercises scattered throughout the book. Hints and solutions are provided
for all exercises.
The exercises are of two types. Some within the chapter, to help motivate and understand the
concepts introduced. Some at the end of the chapter, to help review and consolidate.
Strategy and motivation for all proofs are given to enable diligent readers to work out details on
their own.
All concepts are developed keeping both students and teachers in mind. This book is an
excellent source for self-study. It lays a good foundation for more advanced topics. It has many
ideas, examples and exercises which may be of use to teachers teaching the subject.

Table of Contents 

Preface

1. Metric Spaces
2. Topological Spaces
3. Continuity
4. Closed Sets and Adherent Points
5. Separation Axioms
6. Countability Axioms
7. New Topologies from the Old
8. Compact Spaces
9. Connected and Path-connected Space
10. Locally P spaces
11. Baire’s Theorems and Contraction Principle
12. Homotopy and the Fundamentals Group

A   Hints, Solutions and Answers

Bibliography

Index