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Аннотация: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) = [mindim X,∞], or d-SpU (X) = d-Spβ (X) = {dim X}. If X is not a pseudocompact space, then [dim X,∞] ⊂ d-SpU (X); if X is a Lindelöff non-compact space,
then d-SpU (X) = [dim X,∞]; if X is a separable metrizable non-compact space, then
d-SpW (X) = [mindim X,∞]. 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 mindim X <=n is
proved.