Wadge reducibility in the Baire and Cantor spaces is very important in descriptive set theory. We consider Wadge reducibility in so called φ-spaces which are topological counterpart of the algebraic directed-complete partial orderings. It turns out that in many spaces the Wadge reducibility behaves worse than in the classical case but there exist also interesting examples of spaces with a bette...

In this paper, the concept of pairwise fuzzy globally disconnected spaces is introduced and studied. The condition under which pairwise fuzzy globally disconnected spaces become pairwise fuzzy -Baire spaces, is established. Several characterizations of pairwise fuzzy globally disconnected spaces, are obtained.

Two classes of spaces are studied, namely locally realcompact spaces and HNcomplete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences ...