In this research, we introduce and study the concept of fibrewise bitopological spaces. We generalize some fundamental results from fibrewise topology into fibrewise bitopological space. We also introduce the concepts of fibrewise closed bitopological spaces,(resp., open, locally sliceable and locally sectionable). We state and prove several propositions concerning with these concepts. On the other hand, we extend separation axioms of ordinary bitopology into fibrewise setting. The separation axioms we extend are called fibrewise pairwise T_0 spaces, fibrewise pairwise T_1 spaces, fibrewise pairwise R_0 spaces, fibrewise pairwise Hausdorff spaces, fibrewise pairwise functionally Hausdorff spaces, fibrewise pairwise regular spaces, fibrewise pairwise completely regular spaces, fibrewise pairwise normal spaces, and fibrewise pairwise functionally normal spaces. In addition, we offer some results concerning these extended axioms. Finally, we introduce some concepts in fibrewise bitopological spaces which are fibrewise ij-bitopological spaces, fibrewise ij-closed bitopological spaces, fibrewise ij-compact bitopological spaces, fibrewise ij-perfect bitopological spaces, fibrewise weakly ij-closed bitopological space, fibrewise almost ij-perfect bitopological space, fibrewise ij^*-bitopological spaces. We study several theorems and characterizations concerning these concepts.
A Study of Some Generalizations of Fibrewise Bitopological Spaces
fibrewise closed bitopological spaces
fibrewise open bitopological spaces
fibrewise locally sliceable bitopological spaces
fibrewise locally sectionable bitopological spaces.
Publication Date
Wed Jan 20 2021
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
αg_Ị-open sets and αg_Ị-functions
αg_Ị-closed set
αg_Ị O-functions
αg_Ị C-functions
αg_Ị-continuous function
Strongly αg_Ị-continuous function
αg_Ị-irresolute function
ideal.
The objective of this paper is to show modern class of open sets which is an -open. Some functions via this concept were studied and the relationships such as continuous function strongly -continuous function -irresolute function -continuous function.
Publication Date
Fri Jan 01 2010
Journal Name
Journal Of Collage Of Education
FILTER BASES AND ω-PERFECT FUNCTIONS
closure converge to a point
closure directed toward a set
almost ω-converges to a set
almost condensation point
ω-continuous functions
weakly ω-continuous functions
ω-compact functions
ω-rigid a set
almost ω-closed functions
ω-perfect functions.
In this paper introduce some generalizations of some definitions which are, closure converge to a point, closure directed toward a set, almost ω-converges to a set, almost condensation point, a set ωH-closed relative, ω-continuous functions, weakly ω-continuous functions, ω-compact functions, ω-rigid a set, almost ω-closed functions and ω-perfect functions with several results concerning them.