Absolute C^∗-embedding of F-spaces

Alan Stewart Dow and Ortwin Joachim Martin Forster

Vol. 98 (1982), No. 1, 63–71

DOI: 10.2140/pjm.1982.98.63

Abstract

Let 𝒰 be an open cover of a space X. We define 𝒰 to be a P-cover if each element of 𝒰 is a proper subset of X, 𝒰 is closed under countable unions and for every U ∈𝒰 there is a V ∈𝒰 such that U and X∖V are completely separated. We prove an F-space X is C^∗-embedded in every F-space it is embedded in iff X has no P-covers or X is almost compact.

Mathematical Subject Classification 2000

Primary: 54C45

Secondary: 54G05

Milestones

Received: 28 January 1980

Revised: 2 September 1980

Published: 1 January 1982