A 0-space is a completely
regular Hausdorff space possessing a compactification with zero-dimensional
remainder. In a previous paper the class of almost rimcompact spaces was introduced
and shown to be intermediate between the classes of rimcompact spaces and 0-spaces.
In this paper some properties of almost rimcompact spaces and of 0-spaces are
developed. If X is a space whose non-locally compact part has compact boundary,
then X is a 0-space if and only if X is almost rimcompact. Neither perfect
images or perfect preimages of rimcompact spaces need be 0-spaces. However,
if the perfect preimage of an almost rimcompact space is a 0-space, then
that perfect preimage is almost rimcompact. Subspaces and products are
considered.
