An ascoli theorem for multi-valued functions
1971 ◽
Vol 12
(4)
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pp. 466-472
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The concept of simultaneous or collective continuity of a family of single valued functions was introduced by Gale [3] for regular spaces to replace equicontinuiry in metric spaces. Smithson [6] extended the standard point-open and compact-open function space topologies to include multi-valued functions. The aim of this paper is to use these topologies and extend the notion of collective continuity in order to obtain an Ascoli type theorem for multi-valued functions analogous to Theorem 1 in [3, p. 304]. We have the following theorem in mind:
Keyword(s):
1966 ◽
Vol 9
(3)
◽
pp. 349-352
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2009 ◽
Vol 44
(1)
◽
pp. 159-168
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2010 ◽
Vol 157
(2)
◽
pp. 336-351
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Keyword(s):
1972 ◽
1973 ◽
Vol 39
(1)
◽
pp. 219-219