Download Metric Spaces by Satish Shirali,Harkrishan Lal Vasudeva PDF

By Satish Shirali,Harkrishan Lal Vasudeva

This quantity presents a whole creation to metric area idea for undergraduates. It covers the topology of metric areas, continuity, connectedness, compactness and product areas, and contains effects akin to the Tietze-Urysohn extension theorem, Picard's theorem on usual differential equations, and the set of discontinuities of the pointwise restrict of a series of continuing services. Key positive aspects contain: an entire bankruptcy on product metric areas, together with an explanation of Tychonoff’s Theorem a wealth of examples and counter-examples from actual research, series areas and areas of continuing services a variety of workouts – with ideas to such a lot of them – to check figuring out. the one prerequisite is a familiarity with the fundamentals of genuine research: the authors take care to make sure that no previous wisdom of degree idea, Banach areas or Hilbert areas is thought. the fabric is constructed at a leisurely speed and functions of the speculation are mentioned throughout.

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