Extending functions from products with a metric factor and absolutes

Teodor C. Przymusiński
1982 Pacific Journal of Mathematics  
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 X Z over Y X Z where Z is a metric or a paracompact p-space, respectively. We study the relationship between mX (resp. pX) and the Hewitt realcompactification υX
more » ... tification υX (resp. the Dieudonne completion μX) of X. We show that for normal and countably paracompact spaces mX -υX 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.
doi:10.2140/pjm.1982.101.463 fatcat:frpqhtxqwndbtgddlmoogcjyzq