Mappings and decompositions

George Kenneth Williams

Vol. 45 (1973), No. 1, 387–392

DOI: 10.2140/pjm.1973.45.387

Abstract

If X is a locally connected, locally compact Hausdorff space and R is an equivalence relation on X with fibers which are connected with compact boundaries, then it is known that three types of continuity for R are equivalent. The main result of this note shows that the connectedness of the fibers can be replaced by the requirement that the decomposition be almost proper, i.e., the saturation of each compact set has compact components.

Mathematical Subject Classification 2000

Primary: 54C60

Milestones

Received: 11 November 1971

Revised: 9 June 1972

Published: 1 March 1973