A subspace Y of a space X is said to have the relatively star-K-Menger (resp., relatively star-C-Menger) property in X if for every sequence (Un: n ∈ ω) of open covers of X, there exists a sequence (Kn: n ∈ ω) of compact (resp., countably compact) subsets of X such that (St(Kn, Un): n ∈ ω) forms an open cover of Y. In this paper, we investigate the topological properties of relatively star-K-Menger and relatively star-C-Menger subspaces. We establish a variety of preservation results under natural topological operations, and derive cardinal restrictions by bounding the extent of such subspaces in terms of the classical invariants b and d. Examples demonstrate non-preservation in products and distinctions from related properties, establishing a unified framework for relative star-selection principles.
Singh et al. (Wed,) studied this question.