LAUSR

Abstract Sarsak [On μ \mu -compact sets in μ \mu -spaces, Questions Answers Gen. Topology 31 (2013), no. 1, 49–57] introduced and studied the class of μ \mu -Lindelöf sets in μ \mu -spaces. Mustafa [ μ \mu -semi compactness and μ \mu -semi Lindelöfness in generalized topological spaces, Int. J. Pure Appl. Math. 78 (2012), no. 4, 535–541] introduced and studied the class of μ \mu -semi-Lindelöf sets in generalized topological spaces (GTSs); the primary purpose of this paper is to investigate more properties and mapping properties of μ \mu -semi-Lindelöf sets in μ \mu -spaces. The class of μ \mu -semi-Lindelöf sets in μ \mu -spaces is a proper subclass of the class of μ \mu -Lindelöf sets in μ \mu -spaces. It is shown that the property of being μ \mu -semi-Lindelöf is not monotonic, that is, if ( X , μ ) \left(X,\mu ) is a μ \mu -space and A ⊂ B ⊂ X A\subset B\subset X , where A A is μ B {\mu }_{B} -semi-Lindelöf, then A A need not be μ \mu -semi-Lindelöf. We also introduce and study a new type of generalized open sets in GTSs, called ω μ {\omega }_{\mu } -semi-open sets, and investigate them to obtain new properties and characterizations of μ \mu -semi-Lindelöf sets in μ \mu -spaces.