Abstract
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 d-SpU(X)=[mindimX,∞], or d-SpU(X)=d-Spβ(X)={dimX}. If X is not a pseudocompact space, then [dimX,∞]⊂d-SpU(X); if X is a Lindelöff non-compact space, then d-SpU(X)=[dimX,∞]; if X is a separable metrizable non-compact space, then d-SpW(X)=[mindimX,∞]. 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 mindimX⩽n is proved.
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