  Some reasonings are presented that the problem of a singularity in general
relativity with the problem of freezing of the $5^{th}$ dimension can be
connected. It is shown that some solutions in the 5D Kaluza-Klein gravity with
the cross section in the Planck region have a region $(\approx l_{Pl})$ where
the metric signature changes from $\{+,-,-,-,- \}$ to $\{-,-,-,-,+ \}$. The
idea is discussed that such switching can not occur following some general
point of view that the Planck length is the minimal length in the nature and
consequently the physical quantities can not change very quickly in the course
of this length. In this case the dynamic of the $G_{55}$ metric component
should be frozen.
