  Bi-tensor kernel in integral form of Einstein equations realizing Mach's idea
of non-existence of empty space-times is taken as an inverse of differential
operator ("Mach operator") defined conventionally as a second variation of
Einstein's gravity Action over contravariant components of metric tensor. The
choice of transverse gauge condition used in this definition does not influence
results of the paper since only transverse and traceless tensor modes written
on different background space-times are studied. Presence of ghosts among modes
of Mach operator invalidates the integral formulation of Einstein equations.
And the demand of absence of these ghosts proves to be a selection rule for
dimensionality of the background space-time. In particular Mach operator
written on De Sitter background or on the background of so called "Einstein
Universe" does not possess tensor ghosts only in 4-dimensions. The similar
demand gives non-trivial formula for dimensionalities of subspaces of the
Freund-Rubin background.
