Geodesic
Hausdorff Distance and a Compactness Criterion for Continuous Functions
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 463-468

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DOI

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.
DOI : 10.4153/CMB-1986-073-5
Mots-clés : 40A30, 54B20, 54C35, 54E50, Hausdorff metric, Arzela-Ascoli Theorem, complete metric space, functions with closed graph 
Beer, Gerald. Hausdorff Distance and a Compactness Criterion for Continuous Functions. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 463-468. doi: 10.4153/CMB-1986-073-5
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     title = {Hausdorff {Distance} and a {Compactness} {Criterion} for {Continuous} {Functions}},
     journal = {Canadian mathematical bulletin},
     pages = {463--468},
     year = {1986},
     volume = {29},
     number = {4},
     doi = {10.4153/CMB-1986-073-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-073-5/}
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