Preservation of completeness by some continuous maps (Q977454)

The main result of the paper shows that the image~\(Y\) of a~\(0\)-dimensional paracompact Čech-complete space~\(X\) under a continuous surjection \(f:X\to Y\) which takes clopen sets in~\(X\) to resolvable sets in~\(Y\) is complete if metrizable. Many more completeness conditions of topolological spaces are considered in the paper which apply not only to metrizable spaces. The motivation of the paper was to solve a~question by \textit{A.~V. Ostrovsky} posed in [Topology Appl. 156, No.~9, 1749--1751 (2009; Zbl 1172.54019)]