Separation Axioms in Bitopological Ordered Spaces

Abstract

In this paper, we introduce and study some new type of separation axioms in bitopological ordered spaces via (i, j)-semiopen sets.

SOME NEW SEPARATION AXIOMS VIA gr-b-I-OPEN SETS

“…A regular open sets if A= int cl(A) (for short, r-open) [8] where cl(A) and int(A) refer to the closure operator and the interior operator of the set A, respectively. The δ-interior [9] of a subset A of X is the union of all regular open sets of X contained in A and is denoted by δ-int (A) and the subset A is called δ-open [9] if A=δ-int(A). i.e., a set is δ-open if it is the union of regular open sets.…”

“…Definition 2.2: A subset A of a space X is said to be a. 1-regular b-closed (briefly r-b-closed) [9] if rcl (A) ⊂ U whenever A ⊂ U and U is b-open in X. 2-generalized closed set (briefly g-closed) [4] if cl(A) ⊆ U whenever A ⊆ U and U is open in (X ,τ).…”