Metric Spaces

Piotr Mikusiński and Michael D. Taylor
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Piotr Mikusiński: University of Central Florida, Department of Mathematics
Michael D. Taylor: University of Central Florida, Department of Mathematics

Chapter 2 in An Introduction to Multivariable Analysis from Vector to Manifold, 2002, pp 43-73 from Springer

Abstract: Abstract In the study of analysis in ℝ N (and later on manifolds) we are interested in such things as continuity, differentiability, and integrability. All these ideas depend on limit processes and convergence. Let us glance at some examples of convergence which may be familiar to the reader from a previous study of functions of a single variable. If some of the ideas — for example, Lebesgue integration or uniform convergence — are unfamiliar, this should not be cause for dismay. We are called not so much to appreciate the particular ideas as their variety.

Keywords: Compact Subset; Normed Space; Cauchy Sequence; Contraction Mapping; Convergent Subsequence (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4612-0073-4_2

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