Vol. 34, No. 3, 1970

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Ascoli’s theorem for spaces of multifunctions

You-Feng Lin and David Alon Rose

Vol. 34 (1970), No. 3, 741–747
Abstract

The purpose of this paper is to prove that if X and Y are two arbitrary topological spaces and if M(X,Y ;c) denotes the space of all multi-valued functions on X to Y with the compact-open topology, then a closed set ℱ⊂ M(X,Y ;c) is compact if at each point x X,(x) = ∪{F(x)|F ∈ℱ} has a compact closure in Y , and is evenly continuous.

Mathematical Subject Classification
Primary: 54.28
Milestones
Received: 21 November 1969
Published: 1 September 1970
Authors
You-Feng Lin
David Alon Rose