Local compactness of families of continuous point-compact relations

Worthen N. Hunsacker and Somashekhar Amrith Naimpally

Vol. 52 (1974), No. 1, 101–105

DOI: 10.2140/pjm.1974.52.101

Abstract

The purpose of this paper is to prove that the pointwise closure of an equicontinuous family of point-compact relations from a compact Hausdorff space to a locally compact Hausdorff uniform space is locally compact in the topology of uniform convergence. This is a generalization of a recent result of R. V. Fuller.

Mathematical Subject Classification 2000

Primary: 54C35

Milestones

Received: 27 October 1973

Revised: 8 February 1974

Published: 1 May 1974