Local Compactness in Set Valued Function Spaces

Abstract

Recently Hunsaker and Naimpally [2] have proved: The pointwise closure of an equicontinuous family of point compact relations from a compact T2-space to a locally compact uniform space is locally compact in the topology of uniform convergence. This is a generalization of the same result of Fuller [1] for single valued continuous functions.For a range space which is locally compact normal and uniform theorem B below is an improvement on the result of Hunsaker and Naimpally quoted above [see Remark 3 at the end of this paper].