  It is proved that the Riemann tensor squared is divergent as $\tau \ra 0$ for
a wide class of cosmological metrics with non-exceptional Kasner-like behaviour
of scale factors as $\tau \ra 0$, where $\tau$ is synchronous time. Using this
result it is shown that any non-trivial generalization of the
spherically-symmetric Tangherlini solution to the case of $n$ Ricci-flat
internal spaces \cite{FIM} has a divergent Riemann tensor squared as $R \ra
R_0$, where $R_0$ is parameter of length of the solution. Multitemporal naked
singularities are also considered.
