This is a textbook designed to meet the requirements of undergraduate students in Mathematics. It can be comfortably covered in one semester. The content has been tested in the classroom by several professors over the past four decades and the book has been well received by the student community.
Table of Content
Chapter 1 PRELIMINARIES
1.2 Sets and Functions
1.3 Countable Sets
1.4 Uncountable Sets
1.5 Inequality of Holder and Minkowski
Chapter 2 METRIC SPACES
2.2 Definition and Examples
2.3 Bounded sets in a Metric Space
2.4 Open Ball (Open Sphere) in a Metric Space
2.5 Open Sets
2.7 Interior of a set
2.8 Closed Sets
2.10 Limit Point
2.11 Dense Sets
Chapter 3 COMPLETE METRIC SPACES
3.3 Baire’s Category Theorem
Chapter 4 CONTINUITY
4.4 Uniform Continuity
4.5 Discontinuous Functions on R
Chapter 5 CONNECTEDNESS
5.2 Definition and Examples
5.3 Connected subsets of R
5.4 Connectedness and Continuity
Chapter 6 COMPACTNESS
6.2 Compact Metric Spaces
6.3 Compact Subsets of R
6.4 Equivalent Characterisations for Compactness
6.5 Compactness and Continuity
Chapter 7 The METRIC SPACE C[a; b]
7.2 Pointwise Convergence
7.3 Uniform Convergence
7.4 Test for Uniform Convergence
7.5 The Metric Space C[a; b]
7.6 Weierstrass Approximation Theorem
Chapter 8 CONTRACTION MAPPING AND ITS
8.2 Contraction Mapping Theorem
Chapter 9 COMPLETION OF A METRIC SPACE
• OBJECTIVE TYPE QUESTIONS
About The Authors
Dr. S. Arumugam is currently senior professor (research) and director, National Centre for Advanced research in Mathematics (n-CARDMATH), Kalasalingam Academy of Research and Education, Krishnankoil, India. He has completed 50 years of academic life and has authored 30 books including two textbooks in Tamil. He has organized 27 conferences and workshops and has edited 12 proceedings. He has guided 44 Ph.D candidates and has published around 250 papers in national and international journals. His areas of research interest are graph theory and applications, biological networks, social networks, visual cryptography and topological projective planes. He has served as visiting/adjunct/conjoint professor in several universities in Australia, UK and USA. He has visited more than 20 countries for delivering invited talks in conferences. He is the founder editor-in-chief of AKCE International Journal of Graphs and Combinatorics.
Mr. A. Thangapandi Isaac, who got retired as head of the department of Mathematics, St. John’s College, Palayamkottai has 30 years of experience in teaching. He is also a coauthor of around 20 books along with Professor S. Arumugam.
Dr. A. Somasundaram is presently working as an associate professor at Birla Institute of Technology and Science Pilani – Dubai campus. He is having 22 years of experience in teaching and research in Mathematics. His research areas include fuzzy graphs, domination in graphs and network science. He has to his credit several publications in standard international journals. He is also a coauthor of five textbooks.
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