The covering dimension invariants

In the present paper three types of covering dimension invariants of a space X are distinguished. Their sets of values are denoted by d-SpU(X), d-SpW(X) and d-Spβ(X). One of the exhibited relations between them shows that the minimal values of d-SpU(X), d-SpW(X) and d-Spβ(X) coincide. This minimal value is equal to the dimension invariant mindim defined by Isbell. We show that if X is a locally compact space, then either , or . If X is not a pseudocompact space, then ; if X is a Lindelöff non-compact space, then ; if X is a separable metrizable non-compact space, then . Among the properties of covering dimension invariants the generalization of the compactification theorem of Skljarenko is presented. The existence of compact universal spaces in the class of all spaces X with w(X)⩽τ and is proved.