General Topology: Metric Spaces, Dedekind Cut, Isometries, and Hilbert Cube

This book is dedicated to metric spaces and their topology. The book starts with ZFC axioms. The real number system is constructed by both the Dedekind cut and the Cauchy sequence approach. The various examples and properties of metric spaces and normed linear spaces are discussed. The different distances between the sets are highlighted. The research work on metric-preserving maps and isometries on different p-norms has been discussed. Homeomorphism and different equivalent metrics have also been discussed. A detailed description of a metric on the product and the quotient set is also provided. The completion of a metric space as a universal property and applications of the Baire Category Theorem are covered. A special focus is on compactness and the relation between a compact metric space, the Hilbert Cube, and the Cantor set. The properties of connected and path-connected metric spaces are provided.

Dr. Kakkar got his D.Phil. from University of Allahabad. Currently he is a professor at Central University of Rajasthan, India. He is also a regional coordinator for Mathematical Olympiad Program for Rajasthan conducted by Homi Bhabha Center for Science Education, Tata Institute of Fundamental Research, Mumbai.He was also awarded Start-up grant from UGC, India.