Abstract We introduce the notion of π F ( Δ ) –network and denote the combinatorial principles FELL ( Π F ( Δ ) , Π F ( Δ ) ) and FELL ⁎ ( Π F ( Δ ) , Π F ( Δ ) ) , which will be applied to characterize the spaces X whose hyperspace, endowed with the Fell topology, satisfies the SSR condition and the SR condition. We use the selection principle S S Δ ⁎ ( O , O ) to characterize the SSR property for the spaces K ( X ) , F ( X ) and [ X ] 1 , endowed with the lower Vietoris topology. In addition, we introduce the selection principle S Δ f ( O , O ) to obtain characterizations of the selective versions of metacompactness, mesocompactness and sequential mesocompactness. Finally, we introduce the notion of Δ-moving-off family, which generalizes the one of moving-off family, and we use it to characterize the Rothberger property for certain subspaces of C L ( X ) .

中文翻译：

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超空间上 Rothberger 属性的星型版本

摘要 我们介绍了π F ( Δ ) – 网络的概念，并表示了组合原理FELL ( Π F ( Δ ) , Π F ( Δ ) ) 和FELL ⁎ ( Π F ( Δ ) , Π F ( Δ ) ) , 即将被应用于表征空间 X，其超空间赋予 Fell 拓扑，满足 SSR 条件和 SR 条件。我们使用选择原则 SS Δ ⁎ ( O , O ) 来表征空间 K ( X ) 、 F ( X ) 和 [ X ] 1 的 SSR 属性，这些空间具有较低的 Vietoris 拓扑结构。此外，我们引入了选择原则 S Δ f ( O , O ) 以获得元紧致性、介观紧致性和顺序介观紧致性的选择性版本的特征。最后，我们引入了Δ-moving-off family的概念，它概括了moving-off family，