Embedding compact spaces into compact spaces with few regular open Baire subsets (Q1375162)

\textit{V. V. Fedorchuk} [Sov. Math., Dokl. 15(1974), 1272-1275 (1975); translation from Dokl. Akad. Nauk SSSR 218, 50-53 (1974; Zbl 0355.54013)] constructed a compact first countable space with only two regular open (regular closed) Baire subsets. In the paper under review, the author presents a general construction of spaces with these properties. He shows that, given a compact Hausdorff space \(X\), there exists a compact Hausdorff space \(Y\) such that \(X\) is a retract of \(Y\) and if \(F\) is a regular closed (or regular open) Baire subset of \(Y\), then \(F\) is open (closed). Moreover, if \(X\) is a continuum, \(Y\) is a continuum as well and \(Y\) has only two regular closed (or regular open) Baire subsets.