General Topology and Applications: General Topology

by HEMANT KUMAR PATHAK

Overview

Graduate Texts in Mathemkatics 2

Hemant Kumar Pathak

General Topology and Applications

 

 

This textbook discusses all useful topics in general topology and applications. It contains complete definitions of topics well-explained by suitable examples, explanations, and proofs throughout the book. The book studies major topics on topological spaces and continuous functions, countability, separable spaces and connectedness, compactness and the Tychonoff theorem, separation axioms, compactification, products and coproducts, embedding, metrization theorem and paracompactness, nets and filters, complete metric spaces and function spaces,uniform spaces, manifolds and their geometry, Baire spaces and dimension geometry.

 

This book is designed as a textbook for a two-semester course in point-set topology or metric topology, as well as for a first-semester course in topology at the lower undergraduate level. The book is also accessible to junior mathematics majors who have studied multivariable.

 

Product Details

ISBN-13:	9788195637928
Publisher:	SCIENGER DRAFT
Publication date:	03/07/2024
Series:	Graduate Texts in Mathematics 2 , #2
Sold by:	Barnes & Noble
Format:	eBook
Pages:	506
File size:	129 MB
Note:	This product may take a few minutes to download.

About the Author

Hemant Kumar Pathak has been professor and Head of the School of Studies in Mathematics at the Pt. Ravishankar Shukla University, Raipur, India. He has also been the dean of science, member of standing committee, chairman, UFM Committee, director of the Center for Basic Sciences, and director of the Human Resource Development Centre at the same university. He has previously worked at Kalyan P.G. College, Bhilai Nagar, and the Government Postgraduate College, Dhamtari, India. He has been Vice-Chancellor (President) of Bharti Vishwavidyalaya, Durg. He earned his Ph.D. from Pt. Ravishankar Shukla University, Raipur in 1988.Professor Pathak was awarded the ''Distinguished Service Award 2011" by the Vijnana Parishad of India. He has also been nominated for 3rd Ganita Ratna Award 2023-24. With over 41 years of teaching and research experience, he has published three books, Theory of Functions of Complex Variable (CRC Press, Taylor &Fransis Group), An Introduction to Nonlinear Analysis and Fixed Point Theory (Springer Nature), Complex Analysis and Applications (Springer Nature), and more than 250 research papers in leading international journals of repute on approximation theory, operator theory, integration theory, fixed point theory, number theory, cryptography, summability theory, fuzzy set theory and Banach frames.Professor Pathak currently serve on the editorial boards of American Journal of Computational and Applied Mathematics, Fixed Point Theory and Algorithms for Sciences and Engineering (Springer Nature), and the Journal of Modern Methods in Numerical Mathematics, and as a reviewer for the Mathematical Review of the American Mathematical Society. In addition, he is a life member of the Allahabad Mathematical Society, Bharata Ganita parishad, the Vijana Parishad of India, Calcutta Mathematical Society, and National Academy of Mathematics.

Table of Contents

1. Fundamentals : Basics of Logic, Set THeory, and Analysis
2. Topological Spaces and Continuous Functions
3. Countability, Separable Spaces and Connectedness
4. Compactness and the Tychonoff Theorem
5. Separation Axioms
6. Compactification
7. Products and Coproducts
8. Embedding, Metrization Theorems, and Paracomptness
9. Nets and Filters
10. Complete Metric Spaces and Function Spaces
11. Uniform Spaces
12. Manifolds and its Geometry
13. Baire Spaces and Dimension Theory

References

Index