Ascoli’s theorem for spaces of multifunctions

You-Feng Lin and David Alon Rose

Vol. 34 (1970), No. 3, 741–747

DOI: 10.2140/pjm.1970.34.741

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,ℱ(x) = ∪{F(x)|F ∈ℱ} has a compact closure in Y , and ℱ is evenly continuous.

Mathematical Subject Classification

Primary: 54.28

Milestones

Received: 21 November 1969

Published: 1 September 1970