By using m-open multifunctions from a topological space into an m-space, we establish the unified theory for several weak forms of open multifunctions in the sense of Kuratowski between bitopological spaces.

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

By using m-open functions from a topological space into an m-space, we establish the unified theory for several weak forms of open functions in the sense of Kuratowski between bitopological spaces.

We construct a completely regular ordered space (X, T ,≤) such that X is an I-space, the topology T of X is metrizable and the bitopological space (X, T ♯,T ♭) is pairwise regular, but not pairwise completely regular. (Here T ♯ denotes the upper topology and T ♭ the lower topology of X.)

In this paper, we introduce the concept of H(i) connected ditopological texture space. We develop some basic properties of bicontinuity and connectedness in term of ditopological texture space which will used inH(i) connected ditopological texture space. We have established some correspondence related to known structure such as bitopological space, fuzzy lattice and topological space.

A poset model of a topological space X is a poset P together with a homeomorphism φ : X−→Max(P ) (Max(P ) is the subspace of the Scott space ΣP consisting of maximal points of P ). In [11] (also in [2]), it was proved that every T1 space has a bounded complete algebraic poset model. It is, however still unclear whether each T1 space has a dcpo model. In this paper we give a positive answer to t...

In this paper we introduce the concept of $(1,2)^*$-sb-separated sets and $(1,2)^*$-soft b-connected spaces and prove some properties related to these break topics. Also we disscused the properties of $(1,2)^*$-soft b- compactness in soft bitopological space

the purpose of this paper is to introduce the concept of pairwise f-closedness in bitopological spaces. this space contains both of pairwise strongcompactness and pairwise s-closedness and contained in pairwise quasi h-closedness. the characteristics and relationships concerning this new class ofspaces with other corresponding types are established. moreover, several ofits basic and important p...

In [4], Erné relaxed the concept of sobriety in order to extend theory sober spaces and locally hypercompact situations where directed joins were missing, introduced discussed three kinds non-sober spaces: cut spaces, weakly quasisober spaces. [24], other namely DC space, RD space WD investigated. All these six classes are strictly larger than that this paper, it is shown category all not refle...