Topology of Metric Spaces

Description

TOPOLOGY OF METRIC SPACES gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis.In this second revised and enlarged edition, based on the extensive feedback sent by the readers, some material has been removed, some new material included and nearly all problems are given comments, hints and solutions. Table Of Contents: Preface / Basic Notions / Convergence / Continuity / Compactness / Connectedness / Complete Metric Spaces / Answers, Hints and Solutions / Bibliography / Index. Audience Undergraduate Students Special Features: ?All concepts introduced using the primitive concepts of open balls or open sets?Geometric motivations of concepts, definitions and results?Real life motivations and analogies?Lots of concrete and geometric examples and pictures?Numerous exercises in meaningful contexts, with copious hints to most of them?Typical applications of major results?Attention to the difficulties faced by beginners?Most of the proofs start with the strategy of the proof so as to enable good students ?to work on their own?Prepares the ground for higher aspects of topology and analysis