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.
