Abstract We present classical and modified separation properties for the family of Darboux quasi-continuous upper semicontinuous functions. In particular, we provide the correction a mistake from [15] . In the second part we study connections between separating sets by functions and by sets and apply obtained results to solve the problem given by Kowalewski and Maliszewski in [9] . Moreover, we characterize when it is possible to separate given disjoint subsets of the real line by some special sets.

中文翻译：

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按函数和按集合分隔集合

摘要 我们提出了 Darboux 准连续上半连续函数族的经典和修正分离特性。特别是，我们提供了更正 [15] 中的错误。在第二部分中，我们研究按函数和按集合分离集合之间的联系，并应用所得结果来解决 Kowalewski 和 Maliszewski 在 [9] 中给出的问题。此外，我们描述了何时可以通过一些特殊集合来分离实线的给定不相交子集。