On Certain Covering Properties and Minimal Sets of Bigeneralized Topological Spaces

Abstract

<jats:p>We introduce q-Lindelöf, u-Lindelöf, p-Lindelöf, s-Lindelöf, q-countably-compact, u-countably-compact, p-countably-compact, and s-countably-compact as new covering concepts in bigeneralized topological spaces via q-open sets and u-open sets in bigeneralized topological spaces. Relationships between them are studied. As two symmetries relationships, we show that q-Lindelöf and u-Lindelöf are equivalent concepts, and that q-countably-compact and u-countably-compact are equivalent concepts. We focus on continuity images of these covering properties. Finally, we define and investigate minimal q-open set, minimal u-open set, and minimal s-open sets as three new types of minimality in bigeneralized topological spaces.</jats:p>

Study of Open Sets in Bi-generalized Topological Spaces

“…In this Bi-GTS, separation axioms were defined by several authors [10,19,24,31]. Recently, Ghour [2] introduced certain covering properties and minimal sets in Bi-GTS.…”