Transfinite dimensions Indm

We investigate dimensions Indm (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=Ind2. In particular,(1) IndmX<ω1 for every countable dimensional metrizable compactum X;(2) every normal space X has a compactification bX with wbX=wX and IndmbX⩽IndmX.Moreover, if IndX is defined (respectively IndX is finite), then IndmX is defined (respectively IndmX is finite) for every m.