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An ascoli theorem for multi-valued functions

Published online by Cambridge University Press:  09 April 2009

Vincent J. Mancuso
Vincent J. Mancuso
Affiliation:
St. John's University Jamaica, New York, U.S.A.
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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:

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 4 , November 1971 , pp. 466 - 472
Copyright
Copyright © Australian Mathematical Society 1971

References

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