We introduce the notion of hereditary G-compactness (with respect to interpretation). provide a sufficient condition for poset not be hereditarily G-compact, which we use show that any linear order is G-compact. Assuming long-standing conjecture about unstable NIP theories holds, this implies an theory G-compact if and only it stable (and by result Simon, holds unconditionally $$\aleph _0$$ -ca...

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...