On finite unions of certain \(D\)-spaces (Q2474462)

A \(D\)-space, as defined by Van Douwen [\textit{E. K. van Douwen} and \textit{W. F. Pfeffer}, Pac. J. Math. 81, 371--377 (1979; Zbl 0409.54011)], is a space in which for every assignment, \(x\mapsto U_x\), of neighbourhoods one can find a closed and discrete subset~\(D\) such that \(\{U_x:x\in D\}\) covers the space. The author proves that finite unions of strong \(\Sigma\)-spaces and finite unions of DC-like spaces [\textit{R. Telgársky}, Fundam. Math. 88, 193--223 (1975; Zbl 0311.54025)] are \(D\)-spaces.