Geodesic
Compact Subsets in Function Spaces
Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 461-466

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We wish to study the problem of finding conditions under which a family of maps from one space into another, with a suitable topology, is compact. Some of the results obtained in this direction are in [1; 2; 3]. We propose to give conditions, to be called uniformly regular and regular (the terminology is motivated by [4]), under which "Ascoli" theorems can be proved. These notions turn out to be equivalent to even continuity of Kelley [1, page 235] under such conditions that all the theorems in the section on even continuity in it still hold when in their statements even continuity is replaced by either uniform regularity or regularity (see Theorem A below). 
Kaul, S.K. Compact Subsets in Function Spaces. Canadian mathematical bulletin, Tome 12 (1969) no. 4, pp. 461-466. doi: 10.4153/CMB-1969-057-9
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     title = {Compact {Subsets} in {Function} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {461--466},
     year = {1969},
     volume = {12},
     number = {4},
     doi = {10.4153/CMB-1969-057-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-057-9/}
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