@article{Ghour2022, 
author = {Samer Al Ghour},
title = {On some types of functions and a form of compactness via        ω          s      -open sets},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {2220-2236},
keywords = {ωs-open sets, semi-continuous function, ωs-continuous function, irresolute function, semi-open function, pre-semi-open function, semi-compact},
url = {https://www.sciopen.com/article/10.3934/math.2022126},
doi = {10.3934/math.2022126},
abstract = {In this paper,        ω          s      -irresoluteness as a strong form of        ω          s      -continuity is introduced. It is proved that        ω          s      -irresoluteness is independent of each of continuity and irresoluteness. Also,        ω          s      -openness which lies strictly between openness and semi-openness is defined. Sufficient conditions for the equivalence between        ω          s      -openness and openness, and between        ω          s      -openness and semi-openness are given. Moreover, pre-       ω          s       -openness which is a strong form of        ω          s      -openness and independent of each of openness and pre-semi-openness is introduced. Furthermore, slight        ω          s      -continuity as a new class of functions which lies between slight continuity and slight semi-continuity is introduced. Several results related to slight        ω          s      -continuity are introduced, in particular, sufficient conditions for the equivalence between slight        ω          s       -continuity and slight continuity, and between slight        ω          s       -continuity and slight semi-continuity are given. In addition to these,        ω          s      -compactness as a new class of topological spaces that lies strictly between compactness and semi-compactness is introduced. It is proved that locally countable compact topological spaces are        ω          s       -compact. Also, it is proved that anti-locally countable        ω          s       -compact topological spaces are semi-compact. Several implications, examples, counter-examples, characterizations, and mapping theorems are introduced related to the above concepts are introduced.}
}