[Download] "Metric Spaces" by Satish Shirali & Harkrishan Lal Vasudeva # Book PDF Kindle ePub Free
eBook details
- Title: Metric Spaces
- Author : Satish Shirali & Harkrishan Lal Vasudeva
- Release Date : January 27, 2005
- Genre: Mathematics,Books,Science & Nature,Professional & Technical,Engineering,Physics,
- Pages : * pages
- Size : 7195 KB
Description
This volume provides a complete introduction to metric space theory for undergraduates. It covers the topology of metric spaces, continuity, connectedness, compactness and product spaces, and includes results such as the Tietze-Urysohn extension theorem, Picard's theorem on ordinary differential equations, and the set of discontinuities of the pointwise limit of a sequence of continuous functions. Key features include:
a full chapter on product metric spaces, including a proof of Tychonoff’s Theorem
a wealth of examples and counter-examples from real analysis, sequence spaces and spaces of continuous functions
numerous exercises – with solutions to most of them – to test understanding.
The only prerequisite is a familiarity with the basics of real analysis: the authors take care to ensure that no prior knowledge of measure theory, Banach spaces or Hilbert spaces is assumed. The material is developed at a leisurely pace and applications of the theory are discussed throughout, making this book ideal as a classroom text for third- and fourth-year undergraduates or as a self-study resource for graduate students and researchers.