Projective completeness and projective classes of spaces (Q1107159)

Productivity of (\({\mathcal P},{\mathcal R},{\mathcal F})\)-projective classes is investigated (\({\mathcal P},{\mathcal R}\) are classes of topological spaces, \({\mathcal F}\) is a class of mappings; X is (\({\mathcal P},{\mathcal R},{\mathcal F})\)-projective if Y belongs to \({\mathcal R}\) whenever \(Y\in {\mathcal P}\) and there is \(f: X\to Y\), \(f\in {\mathcal F}\), as defined by \textit{A. V. Arkhangel'skij} [Vestn. Mosk. Univ., Ser. I 1983, No.6, 4-9 (1983; Zbl 0544.54014)]. In the paper, \({\mathcal P}\) are classes close to metrizable spaces, \({\mathcal R}\) close to Čech-complete spaces and \({\mathcal F}\) close to open maps.