Hard pseudocompact spaces

Abstract

The purpose of this paper is to show that hard pseudocompact spaces are indeed a significant generalisation of pseudocompact spaces on one hand and realcompact spaces on the other. To achieve this we have provided four intrinsic characterisations of hard pseudocompact spaces, which was absent in the literature. Finally, under smallness restrictions on hyper-real remainder of the Stone Cěch compactification of a Tychonoff space we have achieved in producing a representation for hard pseudocompact space.