Metric Spaces by Satish Shirali,Harkrishan Lal Vasudeva

Off Functional Analysis

By Satish Shirali,Harkrishan Lal Vasudeva

This quantity presents a whole creation to metric house conception for undergraduates. It covers the topology of metric areas, continuity, connectedness, compactness and product areas, and comprises 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 capabilities. Key gains comprise: an entire bankruptcy on product metric areas, together with an evidence of Tychonoff’s Theorem a wealth of examples and counter-examples from genuine research, series areas and areas of continuing services quite a few routines – with suggestions to such a lot of them – to check knowing. the single prerequisite is a familiarity with the fundamentals of genuine research: the authors take care to make sure that no past wisdom of degree thought, Banach areas or Hilbert areas is thought. the fabric is constructed at a leisurely velocity and purposes of the speculation are mentioned throughout.

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