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Hausdorff Distance and a Compactness Criterion for Continuous Functions

Published online by Cambridge University Press:  20 November 2018

Gerald Beer
Gerald Beer*
Affiliation:
Department of Mathematics California State University, Los Angeles Los Angeles, California 90032
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Abstract

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Let 〈X, dx〉 and 〈Y, dY〉 be metric spaces and let hp denote Hausdorff distance in X x Y induced by the metric p on X x Y given by p[(x1, y1), (x2, y2)] = max ﹛dx(x1, x2),dY(y1, y2)﹜- Using the fact that hp when restricted to the uniformly continuous functions from X to Y induces the topology of uniform convergence, we exhibit a natural compactness criterion for C(X, Y) when X is compact and Y is complete.

Keywords

40A3054B2054C3554E50Hausdorff metricArzela-Ascoli Theoremcomplete metric spacefunctions with closed graph
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 463 - 468
Copyright
Copyright © Canadian Mathematical Society 1986

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