Recently Bukovský, Das and Šupina [ Ideal quasi - normal convergence and related notions , Colloq. Math. 146 (2017), 265–281] started the study of sequence selection properties (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) of C p ( X ) using the double ideals, where 𝓘 and 𝓙 are the proper admissible ideals of ω , which are motivated by Arkhangeľskii local α i -properties [ The frequency spectrum of a topological space and the classification of spaces , Dokl. Akad. Nauk SSSR 13 (1972), 1185–1189]. In this paper, we obtain some characterizations of (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) properties of C p ( X ) in the terms of covering properties and selection principles. Under certain conditions on ideals 𝓘 and 𝓙, we identify the minimal cardinalities of a space X for which C p ( X ) does not have (𝓘, 𝓙- α 1 ) and (𝓘, 𝓙- α 4 ) properties.

中文翻译：

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具有双重理想的Cp（X）中的序列选择属性

最近，Bukovský，Das和Šupina[理想准-正规收敛和相关概念，Colloq。数学。146（2017），265–281]使用双重理想开始了C p（X）的序列选择特性（𝓘，𝓙-α1）和（𝓘，𝓙-α4）的研究，其中the和the是由Arkhangeľskii局部αi -properties [拓扑空间的频谱和空间的分类，Dokl。阿卡德 Nauk SSSR 13（1972），1185–1189]。在本文中，我们从覆盖特性和选择原理方面获得了C p（X）的（𝓘，𝓙-α1）和（𝓘，𝓙-α4）性质的一些表征。在理想条件𝓘和certain的某些条件下，我们确定C p（X）不具有（𝓘，𝓙-α1）和（𝓘，𝓙-α4）性质的空间X的最小基数。