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In this paper,we introduced the star version of the Hurewicz basis covering property,studied by Babinkostova, Ko?cinac, and Scheepers in 2004. The authors obtained the relationship between star-selection principles and the star version of the Hurewicz basis covering property for metrizable spaces. We also consider the star version of Hurewicz measure zero spaces and characterized these new spaces by the star-selection principle related to star-Hurewicz spaces.

Star versions of the Hurewicz basis covering property and strong measure zero spaces