Note on the spaces P(S) of regular probability measures whose topology is determined by countable subsets

Roman Pol

Vol. 100 (1982), No. 1, 185–201

DOI: 10.2140/pjm.1982.100.185

Abstract

Two closely connected topics are discussed: countable tightness in the spaces P(S) of regular probability measures with the weak topology and a convex analogue to Lindelöf property of the weak topology of the function spaces C(S) defined by H. H. Corson. The main result of this note exhibits a rather wide class of compact spaces stable under standard operations including the operation P(S), such that within this class both of the properties we deal with are dual each other and they behave in a regular way. Some related open problems are stated.

Mathematical Subject Classification 2000

Primary: 54C35

Secondary: 46E27, 47B38

Milestones

Received: 14 January 1980

Revised: 9 February 1981

Published: 1 May 1982