Some classes of weakly infinite-dimensional spaces

Abstract

A new class of m-C-spaces is introduced and studied. The 2-C-spaces coincide with the spaces weakly infinite-dimensional in the sense of Alexandroff, and the compact ∞-C-spaces are Haver's C-spaces. Special attention is given to the behavior of the dimensional properties of such spaces under continuous maps. An important role is played by d-scattered maps, which are generalizations of fully closed maps.

On the t-equivalence relation

“…We should recall the following two definitions (see [4] and [6]). It is known that a normal space is weakly infinite-dimensional if and only if it is a 2-C-space (see [6]). It is clear that we have the following sequence of inclusions…”

“…It is known that a normal space is weakly infinite-dimensional if and only if it is a 2-C-space (see [6]). It is clear that we have the following sequence of inclusions weakly infinite-dimensional = 2-C ⊇ 3-C ⊇ .…”