We introduce q-Lindelof, u-Lindelof, p-Lindelof, s-Lindelof, 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-Lindelof and u-Lindelof 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.

中文翻译：

---

关于双广义拓扑空间的某些覆盖性质和极小集

我们引入 q-Lindelof、u-Lindelof、p-Lindelof、s-Lindelof、q-countably-compact、u-countably-compact、p-countably-compact 和 s-countably-compact 作为双广义拓扑空间中的新覆盖概念通过双广义拓扑空间中的 q-open 集和 u-open 集。研究它们之间的关系。作为两个对称关系，我们证明 q-Lindelof 和 u-Lindelof 是等价概念，q-countably-compact 和 u-countably-compact 是等价概念。我们专注于这些覆盖属性的连续性图像。最后，我们将最小 q-open 集、最小 u-open 集和最小 s-open 集定义和研究为双广义拓扑空间中的三种新型极小性。