The aim of the present paper is to study connectedness in bitopological ordered spaces and in ideal bitopological ordered spaces.

Given two points p and q of the Sierpinski universal plane curve S, necessary and/ or sufficient conditions are discussed in the paper under which there is a mapping I of S onto itself such that I(P) = q and I belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.

The bitopological unstability of RR-pairwise paracompactness in presence of pairwise Hausdorff separation axiom is caused by a bitopological property which is much weaker and more local than RR-pairwise paracompactness. We slightly generalize some Michael’s constructions and characterizeRR-pairwise paracompactness in terms of bitopological θ-regularity, and some other weaker modifications of pa...

A considerable problemof some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiom τS2σ which is appropriate for the study of the bit...

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 of spaces with other corresponding types are established. Moreover, several of its basic and important...

In this present paper, by utilizing ij−δ semi open sets, we introduce ij−∧δ, ij−∨δ, g− ij−∧δ, g− ij−∨δ sets and investigate some of their properties in bitopological spaces. Also, we present and study the notions of ij − T∨sδ space, ij−∧δ continuous, ij−∧δ irresolute, ij−∧δ open and ij−∧δ homeomorphism functions.

Localization due to space structure, rather than due to randomness, is investigated by studying the usual tight-binding model on the Sierpinski gasket. Some exact results are obtained from the decimation —renormalization-group method. It is surprising that there exist an infinite number of extended states on the Sierpinski gasket. This set of extended states forms a Cantor set. The rest of the ...

The main objectives of this paper are to introduce the concept pairwise countably compact in bitopological space,and we some generalization spaces, and their properties, relate it other spaces.

In this paper, we give and study different types of separation axioms using the remoted neighbourhood of a fuzzy point and a fuzzy set in the fuzzy supratopological Spaces (X, s τ ) which is generated by the fuzzy bitopological space (X, 1 2 , τ τ ). Several properties on these separation axioms are researched.