Vol. 98, No. 1, 1982

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Absolute Cāˆ—-embedding of F-spaces

Alan Stewart Dow and Ortwin Joachim Martin Forster

Vol. 98 (1982), No. 1, 63ā€“71

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 XV 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
Received: 28 January 1980
Revised: 2 September 1980
Published: 1 January 1982
Alan Stewart Dow
Ortwin Joachim Martin Forster