Note on \(s\)-expandable spaces (Q6057440)

The semi-closure of a subset \(A\) of a topological space \(X\) is denoted by \(\text{sCl}(A)\). In this paper, the author gives an example showing there are subsets \(G, H\) of a topological space \(X\) such that \(\text{sCl}(G)\cup\text{sCl}(H)\neq\text{sCl}(G\cup H)\). And, it is shown that if \(\mathcal{F}=\{F_j: j\in J\}\) is semi-locally finite collection of an extremally disconnected space \(X\), then \(\bigcup_{j\in J}\text{sCl}(F_j)=\text{sCl}(\bigcup_{j\in J}F_j)\), where a collection \(\mathcal{F}\) of \(X\) is said to be semi-locally finite if for each \(x\in X\) there is a semi-open set \(G\) satisfying that \(x\in G\) and the subcollection \(\{F\in\mathcal{F}: G\cap F\neq\emptyset\}\) is finite.