On Menger Spaces in Generalized Topology

We introduce new types of covering properties in generalized topology, namely; -Menger and -uniformly Menger spaces, and investigate their fundamental properties. To achieve this, we replace open sets in the definition of the standard Manger spaces with -open sets of generalized topological spaces. The results show that the -Menger property is stronger than the Menger property. Additionally, -Menger spaces are preserved when forming subspaces and countable unions. We also characterize -uniformly Menger spaces and study their relationship with -Menger spaces. Examples are given to further illustrate our results.