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1 results

  • Hausdorff Distance and a Compactness Criterion for Continuous Functions

  • Gerald Beer
  • Journal:
    Canadian Mathematical Bulletin / Volume 29 / Issue 4 / 01 December 1986
    Published online by Cambridge University Press:
    20 November 2018, pp. 463-468
    Print publication:
    01 December 1986
    • Article
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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.