We study preservation properties of relatively star-Hurewicz property under two mappings and in Alexandroff space. For a topological space X, the collection of relatively star-Hurewicz subspaces of X is an admissible \(\sigma\)-ideal in X. The characterizations of relatively star-Hurewicz spaces given using selection principles. For a paracompact space X, TWO has a winning strategy in the star-Hurewicz game on X if and only if TWO has a winning strategy in the Hurewicz game on X. In this manner we obtain relationships of relatively star-Hurewicz property with other existing Hurewicz properties in literature.

我们研究了两个映射下和Alexandroff空间中相对恒星-Hurewicz性质的保存性质。对于一个拓扑空间X，相对星Hurewicz子空间的集合X是可容许\（\西格玛\） -理想中的X。使用选择原理给出相对恒星-Hurewicz空间的特征。对于超紧凑型空间X，当且仅当TWO在X的Hurewicz游戏中具有获胜策略时，TWO才在X的星-Hurewicz游戏中具有获胜策略。通过这种方式，我们获得了相对恒星-Hurewicz属性与文献中其他现有Hurewicz属性的关系。