Geodesic
Finite spaces and the universal bundle of a group
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 791-799.

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We find sufficient conditions for a cotriad of which the objects are locally trivial fibrations, in order that the push-out be a locally trivial fibration. As an application, the universal $G$-bundle of a finite group $G$, and the classifying space is modeled by locally finite spaces. In particular, if $G$ is finite, then the universal $G$-bundle is the limit of an ascending chain of finite spaces. The bundle projection is a covering projection.
Classification : 54B15, 54B17, 55R35, 55R40, 55R65
Keywords: covering projection; fibration; finite space; push-out 
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Witbooi, Peter. Finite spaces and the universal bundle of a group. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 4, pp. 791-799. http://geodesic.mathdoc.fr/item/CMUC_1997__38_4_a13/