Abstract
The purpose of this paper is to study a new types of compactness in the dual bitopological spaces. We shall introduce the concepts of L-pre- compactness and L-semi-P- compactness .
Highlights
The concepts of bitopological space was initiated by Kelly[1].A set X
A int cl A, the family of all pre open subsets of X is denoted by PO(X).The complement of a pre-open set is called pre-closed set, the family of all pre- closed subsets of X is denoted by PC(X) [2].The smallest pre- closed subset of X containing A is called “pre-closure of A” and is denoted by pre-cl(A)[3]
Let X, be a topological space, a subset A of X is said to be “semi-P-open” set if and only if there exists a pre-open subset U of X. Such that U A pre cl U, the family of all semi –p-open subsets of X is denoted by SPO(X).The complement of a semi-p-open set is called “semi-pclosed” set, the family of all semi-pclosed subsets of X is denoted by SPC(X)
Summary
The concepts of bitopological space was initiated by Kelly[1].A set X equipped with two topologies and is called a bitopological space 2 denoted by. Definition (2.1): Let be a bitopological space and let G be a subset of X. G is said to be: 1- “ L-pre-open” set if and only if there exists a -pre-open set U such that U G cl 2 U .The family of all L-pre-open sub sets of X is denoted by. 2- “ L-semi-P-open” set if and only if there exists a - semi-P-open setU such that U G cl 2 U .The family of all L- semi-P-open sub sets of X is denoted by Definition (2.2): Let be a bitopological space and let A be a subset of X. Remark (2.5): Every -pre-open( -semi- popen) cover of a sub set of a bitopological space is an L. A bitopological space is said to be : 1- “L-pre-compact space ” if and only if every L-pre-open cover of X has a finite sub cover.
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