A characterization of the free actions of zero-dimensional compact groups on fe-dimensional Menger compacta

摘要

This paper contains a theorem characterizing free actions of a zero-dimensional compact group G on a fc-dimensional Menger compactum nk: two free actions a: G x y.k and a: G are equivalent provided that the dimensions of the orbit spaces are equal to k and the actions are strongly universal with respect to the class of free compacta Y with dim(Y/(7) < k. This theorem, as well as-other results of the paper, suggest that, in the category : of compact spaces equipped with free actions of groups of the above type, there are distinguished objects (referred to in what follows as free Menger compacta fik), with properties analogous to those of the classical Menger compacta.