We present a strongly compact version of the Supercompact Magidor forcing ([3]). A variation of it is used to show that the following is consistent: V ⊇ W are transitive models of ZFC+GCH with the same ordinals such that: 1. κ is an inaccessible in W , 2. κ changes its cofinality to ω1 in V witnessed by a club ⟨κα | α < ω1⟩, 3. for every α < ω1, (κ ++ α ) W < κα , 4. (κ++)W = κ+. 1 Preliminary ...

In this paper, some characterizations of fuzzifying strong compactness are given, including in terms nets and presubbases. Several locally the framework topology introduced mapping theorems obtained.

The concept of pairwise S-closedness in bitopological spaces has been introduced and some properties of such spaces have been studied in this paper. EY WORDS AND PHRASES. Pairwise semi-open, Pairwise almost compact, Pairwise S-closed, Pairwise regularly open and regularly closed, Pairwise extremal disconnectedness, Pairwise semi-continuous and irresolute functions. 1980 AMS MATHEMATICS SUBJECT ...

ABSTARCT: We define and characterize a fuzzy pairwise strongly pre-continuous mappings on a fuzzy bitopological space. We investigate some of their properties. We establish some equivalent conditions of fuzzy pairwise strongly precontinuous mappings on a fuzzy bitopological space.

Let L be the space of line transversals to a nite family of pairwise disjoint compact convex sets in R 3. We prove that each connected component of L can itself be represented as the space of transversals to some nite family of pairwise disjoint compact convex sets.

A topological space X, τ is said to be strongly compact if every preopen cover of X, τ admits a finite subcover. In this paper, we introduce a new class of sets called N-preopen sets which is weaker than both open sets and N-open sets. Where a subset A is said to be N-preopen if for each x ∈ A there exists a preopen set Ux containing x such that Ux − A is a finite set. We investigate some prope...