On certain constructions in finitistic spaces
A paracompact Hausdorff space X is said to be finitistic provided every open covering of X admits a finite-dimensional refinement [\textit{R. G. Swan}, Comment. Math. Helv. 34, 1-16 (1960; Zbl 0144.226)]. The authors study sufficient (necessary) conditions for which the direct product \(X\times Y\) of two finitistic spaces is finitistic. For instance, this is the case if X is compact and finite-dimensional. Moreover, it is shown that the adjunction space \(X\cup_ fY\) of a map f:\(A\to Y\), \(A\subseteq X\), is finitistic provided the spaces X and Y are finitistic.
scientific article; zbMATH DE number 3855981