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.

Study on properties of general Sierpinski fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. Like other fractals, general Sierpinski fractals are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. In [22], the authors the geometric modelling of a class of general Sierpinski fractals and their geometric ...

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...

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...