2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78956We show that for each countable simplicial complex P the following conditions are equivalent: (1) $P \in AE(X)$ iff $P \in AE(βX)$ for any space X; (2) There exists a P-invertible map of a metrizable compactum X with $P \in AE(X)$ onto the Hilbert cube.General Topology54F45; 55M10text