English | 2025 | Original PDF, EPUB | 35 MB | 246 Pages
Vipul Kakkar, B0DTFRDL8N, 3111636062, 3111636194, 9783111636061, 9783111636191, 9783111636085, 978-3111636061, 978-3111636191, 978-3111636085
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.