We establish coincidence of major types of dimensions for a broad
class of separable metric spaces with finite borel measures.
To do this we introduce a new type of separable metric spaces,
so called tight spaces, for which these dimensions coincide naturally.
This class includes, for example, all manifolds of the curvature bounded
from below and any their subsets with induced metric.
In particular, we prove that Hentshel-Procaccia and Renyi spectra
for dimensions are equal in tight spaces for any measure.
We also give the examples that demonstrate that all known dimensions
can differ for bad enough metric spaces.