On selectively star-ccc spaces (Q2217222)

This paper introduces the class of selectively star-ccc spaces, a selective variation of the countable chain condition by means of the star operator, discussing how this property relates to other well known covering properties. More precisely, a topological space \(X\) is said to be selectively star-ccc if for every open cover \(\mathcal{U}\) of \(X\) and every sequence of \((A_n:n\in\mathbb{N})\) of maximal families of pairwise disjoint open sets, there is a sequence \((U_n:n\in\mathbb{N})\) such that for every \(n\in\mathbb{N}\), \(U_n\in A_n\) and \(\operatorname{St}\left(\bigcup_{n\in\mathbb{N}}U_n,\mathcal{U}\right)=X\). Selectively star-ccc spaces simultaneously generalize (selective) ccc spaces and Lindelöf spaces, being a strictly larger class as shown by the examples provided in the paper. Other properties of these spaces are discussed, such as the preservation under continuous functions. Further remarks concerning iterations of the star operator are highlighted by the end of the paper.