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What Is Distance? (Popular Lectures in Mathematics) | Yu. A. Shreider

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What Is Distance? (Popular Lectures in Mathematics)

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Author: Yu. A. Shreider

Added by: mirtitles

Added Date: 2021-11-08

Publication Date: 1974

Subjects: mathematics, soviet, distance, geodesics, elementary distance, definition, space, metric spaces, multi-dimensional spaces, norms More

Collections: mir-titles, additional collections

Pages Count: 300

PPI Count: 300

PDF Count: 1

Total Size: 17.80 MB

PDF Size: 3.43 MB

Extensions: epub, pdf, gz, html, zip, torrent

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Downloads: 2.21K

Views: 52.21

Total Files: 16

Media Type: texts

Description

This introduction to the theory of metric spaces carries the student through the motivation, development, and application
of an abstract mathematical concept. Yu. A. Shreider begins with a definition of mathematical concepts and then, to motivate his definition of “ metric space,” the author evaluates distance functions and their properties in elementary geometry. After introducing two sets of metric space axioms, he surveys the properties of open balls, sequences, Cauchy sequences, complete metric spaces, and isometries. In the following chapter, the author offers a number of informative examples.
Professor Shreider turns next to applications of the theories, especially the theory of coding and cybernetics. Then returning to theory, the author defines an n-dimensional vector space over real numbers and develops the theory of norms and metrics
on Euclidean n-space. The final chapter considers the possibility of generalizing the concept of metric space.
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