Weakly and Nearly Countably Compactness in Generalized Topology

Abstract

We define the notions of weakly μ-countably compactness and nearly μ-countably compactness denoted by Wμ-CC and Nμ-CC as generalizations of μ-compact spaces in the sense of Csaśzaŕ generalized topological spaces. To obtain a more general setting, we define Wμ-CC and Nμ-CC via hereditary classes. Using μθ-open sets, μ-regular open sets, and μ-regular spaces, many results and characterizations have been presented. Moreover, we use the properties of functions to investigate the effects of some types of continuities on Wμ-CC and Nμ-CC. Finally, we define soft Wμ-CC and Nμ-CC as generalizations of soft μ-compactness in soft generalized topological spaces.