Transfinite dimensions

We investigate dimensions Ind m (m is an integer ⩾2 or m = ∞ ) introduced in [V.V. Fedorchuk, Weakly infinite-dimensional spaces, Uspekhi Mat. Nauk 62 (2) (2007) 109–164]. These dimensions have intrinsic properties similar to those of the classical transfinite dimension Ind = Ind 2 . In particular, d m X < ω 1 for every countable dimensional metrizable compactum X; ery normal space X has a compactification bX with w b X = w X and Ind m b X ⩽ Ind m X . er, if IndX is defined (respectively IndX is finite), then Ind m X is defined (respectively Ind m X is finite) for every m.