Abstract In this paper, we study some new selection principles using the star operator which was introduced by Bal and Bhowmik (2017) [7] . If the Alexandroff duplicate A ( X ) of a space X has the property U 1 ⋆ ( O , O ) ( U f i n ⋆ ( O , O ) ), then X has the property U 1 ⋆ ( O , O ) ( U f i n ⋆ ( O , O ) ). If a space has the property U f i n ⋆ ( O , O ) , then its inverse image under perfect open map has the property U f i n ⋆ ( O , O ) . The product of a space having U f i n ⋆ ( O , O ) property with σ-compact has the property U f i n ⋆ ( O , O ) . If for each k, X k has the property U 1 ⋆ ( O , O ) ( U f i n ⋆ ( O , O ) ), then X has the property U 1 ⋆ ( O , O w g p ) ( U f i n ⋆ ( O , O w g p ) ). If a subspace A of a space X is weakly Menger (weakly Rothberger), then C l ( A ) has the property U f i n ⋆ ( O , O g p ) ( U f i n ⋆ ( O , O g p ) ). The above-mentioned results answer two published open questions of Song and Xuan from [10] .

中文翻译：

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拓扑学中新的选星原则

摘要 在本文中，我们使用 Bal 和 Bhowmik (2017) [7] 引入的星型算子研究了一些新的选择原则。如果空间 X 的 Alexandroff 副本 A ( X ) 具有属性 U 1 ⋆ ( O , O ) ( U fin ⋆ ( O , O ) )，则 X 具有属性 U 1 ⋆ ( O , O ) ( U fin ⋆ ( O , O ) )。如果一个空间的性质为 U fin ⋆ ( O , O ) ，那么它在完全开映射下的逆图像具有性质 U fin ⋆ ( O , O ) 。具有 U fin ⋆ ( O , O ) 性质的空间与 σ-compact 的乘积具有性质 U fin ⋆ ( O , O ) 。如果对于每个 k，X k 具有属性 U 1 ⋆ ( O , O ) ( U fin ⋆ ( O , O ) )，则 X 具有属性 U 1 ⋆ ( O , O wgp ) ( U fin ⋆ ( O , O wgp ) )。如果空间 X 的子空间 A 是弱 Menger（弱 Rothberger），则 C l ( A ) 具有性质 U fin ⋆ ( O , O gp ) ( U fin ⋆ ( O , O GP ) )。上述结果回答了 [10] 中宋和轩的两个公开问题。