Almost rimcompact spaces (Q1819403)

A space X is a 0-space if it has a compactification with zero-dimensional remainder. In addition, X is rimcompact if it has an open base with compact boundaries. It is known that every rimcompact space is a 0-space. The author defines a space X to be almost rimcompact if X has a compactification in which each point of the remainder has a basis of open sets whose boundaries are contained in X. Clearly, rimcompact implies almost rimcompact implies 0-space. The author presents among other things examples showing that these implications cannot be reversed.