In this article, we have introduced the notion of pairwise Compactness in bi-isotonic spaces via finite intersection property and pairwise open cover. Moreover, we have given pairwise Compactness of bi-isotonic subspaces with both reduced closure and interior functions. We have characterized pairwise Compactness by the neighborhood concept; however, the axioms of bi-isotonic spaces are insufficient to prove the theorem, and we have studied this in bi-closure spaces. For similar reasons, occasionally, bi-closure spaces have been considered with additional explanations, even if some concepts related to Compactness have been naturally extended to bi-isotonic spaces. Additionally, interesting results have been obtained considering the pairwise Hausdorffness and Compactness relationship. It has also been observed that resembling cross-relationships exist for closed subsets of pairwise compact spaces. Finally, it has been observed that the pairwise Compactness of bi-closure spaces is preserved under bi-continuity.

In this paper, we present the notion of weakly compact topo-logical fuzzes and give some characterizations of them. In particular, a characterization of weakly Compactness are given by the closedness of the projection fuzz maps. Also, we study some properties of proper fuzz maps as an important class of closed fuzz maps.

It is well known that, for Hausdorff spaces, a quotient map f : X -> Y is product stable, in the sense that the product map f x g is a quotient map, for every quotient map g, if and only if Y is locally compact and f is biquotient. Here, we present a generalization of those quotient maps which are product stable. 

Some criteria for approximative Compactness of every weakly* closed convex set of Orlicz function spaces equipped with the Luxemburg norm are given. Although, criteria for approximative Compactness of Orlicz function spaces equipped with the Luxemburg norm were known, we can easily deduce them from our main results.