In this paper, we introduced relatively star-C-Hurewicz property in topological spaces following the approach of Bonanzinga and Pansera (Acta Math Hungar 117(3):231–243, 2007) and Guido and Kočinac (Quest Answ Gen Topol 19:107–114, 2001). A subspace A of a topological space X is said to have relatively star-C-Hurewicz property in X (in short, RSCH) or relatively star-C-Hurewicz subspace of X if for each sequence \(\left<{\mathcal {U}}_n : n \in \omega \right>\) of open covers of X there is a sequence \(\left<A_n : n \in \omega \right>\) of countably compact subsets of X such that \(x \in A\) belongs to \(St(A_n, {\mathcal {U}}_n)\) for all but finitely many n. It is shown that relatively star-C-Hurewicz property is hereditary. In this manner, we obtained relationships of relatively star-C-Hurewicz property with other existing Hurewicz properties in the literature.

中文翻译：

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拓扑空间中Star-C-Hurewicz性质的相对化

在本文中，我们采用Bonanzinga和Pansera（Acta Math Hungar 117（3）：231–243，2007）和Guido andKočinac（Quest Answ Gen Topol 19：107）的方法，在拓扑空间中引入了相对于恒星C -Hurewicz的性质。 –114，2001）。子空间甲一个拓扑空间的X被认为具有相对星形Ç -Hurewicz在属性X（简言之，RSCH）或相对星形Ç -Hurewicz的子空间X如果对于每个序列\（\左<{\ mathcal { U}} _ n：X的开封封面的\\ omega \ right> \ n中有一个序列\（\ left <A_n：\ omega \ right> \ n的n的数紧子集的X，使得\（X \在A \）属于\（ST（A_N，{\ mathcal【U}} _ n）的\）为所有，但有限多个Ñ。结果表明，相对恒星的C -Hurewicz性质是遗传的。通过这种方式，我们获得了相对恒星C -Hurewicz性质与文献中其他现有Hurewicz性质之间的关系。