The Baire-category method in some compact extension problems
Elżbieta Pol · Pacific Journal of Mathematics · 1986
We characterize metrizable separable spaces X such that almost every, in the sense of Baire category, embedding h of X into the Hilbert cube I ω provides a compact extension h(X) such that the remainder h(X) \h(X) has certain dimensional property (for instance, is ^-dimensional, countable-dimensional or "metrically weakly infinitedimensional")* We obtain a characterization of metrizable separable spaces which have large transfinite dimension by means of compactifications.Two examples related to the results mentioned above are constructed.