Let [n]:={1,2,…,n} and let a k-set denote set of cardinality k. A family sets is union-closed (UC) if the union any two in also family. Frankl’s conjecture states that for nonempty UC F⊆2[n] such F≠{∅}, there exists an element i∈[n] contained at least half F, where 2[n] denotes power on [n]. The 3-sets Morris smallest number distinct (whose n-set) ensure satisfied (in contains them ⌊n/2⌋+1 all ...

This study introduce a new type of closed sets in topology called Generalized h-closed (briefly, gh-closed) define as follow: E ⊆ χ be gh-closed set if CLh (E)⊆ U whenever and is open (χ,τ). The relation between other classes ( h-closed, g-closed, g -closed, g-closed αg-closed) are studied. Also, the notion gh-continuous mapping on topological space some properties proved. Finally, separation a...

In this paper we have introduced a new class of closed in topological spaces called g**-closed sets and study some its properties . Further introduce the concept g**-continuous functions , g**-irresolute As an application two news paces namely T **-space, **T - space .Further, g**-continuous, mappings are also investigated

The aim of this paper is to introduce the concept of generalized regular closed sets and study some of its properties . The corresponding topological space formed by the family of these sets is also studied. It may be noted that regular closed set doesn’t forms even a supra topological space. Various researchers had studied the concept of generalized closed sets and regular generalized closed s...

In this paper, we study the class of generalized b-closed sets and use this notion to consider new weak and stronger forms of continuities associated with these sets. We apply these notions to give new characterization of extremally disconnected spaces and also Tgs-spaces. 2000 Mathematics Subject Classification: 54A10, 54C8, 54C10, 54D10

A dcpo P is continuous if and only if the lattice C(P ) of all Scottclosed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C(P ). In this paper, we study the order-theoretic properties of C(P ) for general dcpo’s P . The main results are: (i) every C(P ) is C-continuous; (ii) a complete lattice L is iso...