Vol. 101, No. 2, 1982

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Extending functions from products with a metric factor and absolutes

Teodor C. Przymusiński

Vol. 101 (1982), No. 2, 463–475

Extendability of continuous functions from products with a metric or a paracompact p-space factor is studied. We introduce and investigate completions mX and pX of a completely regular space X defined as “largest” spaces Y containing X as a dense subspace such that every continuous real-valued function extends continuously from X × Z over Y × Z where Z is a metric or a paracompact p-space, respectively. We study the relationship between mX (resp. pX) and the Hewitt realcompactification vX (resp. the Dieudonné completion μX) of X. We show that for normal and countably paracompact spaces mX = vX and pX = μX, but neither normality nor countable paracompactness alone suffices. The relationship between completions mX and pX and the absolute EX of X is discussed.

Mathematical Subject Classification 2000
Primary: 54C20
Secondary: 54B10, 54D35
Received: 21 May 1980
Revised: 20 February 1981
Published: 1 August 1982
Teodor C. Przymusiński