Ultrafilters and mappings

Takesi Isiwata

Vol. 104 (1983), No. 2, 371–389

DOI: 10.2140/pjm.1983.104.371

Abstract

We give characterizations of closed, quasi-perfect, d-, Z-, WZ-, W^∗-open, N-, WN-, W_rN- and other maps using closed or open ultrafilters and investigate relations between these maps and various properties as generalizations of realcompactness, i.e., almost-, a-, c- and wa-real compactness, cb^∗-ness and weak cb^∗-ness. Finally we establish several theorems about the perfect W^∗-open image of a weak cb^∗ space and its application to the absolute E(X) of a given space X.

Mathematical Subject Classification 2000

Primary: 54C10

Secondary: 54D30

Milestones

Received: 21 April 1981

Revised: 5 August 1981

Published: 1 February 1983