  {\bf Construction.} For a dominating polynomial mapping {$F: K^n\to K^l$}
with an isolated critical value at 0 ($K$ an algebraically closed field of
characteristic zero) we construct a closed {\it bundle} $G_F \subset T^{*}K^n
$. We restrict $ G_F $ over the critical points $Sing(F)$ of $ F$ in $
F^{-1}(0)$ and partition $Sing(F)$ into {\it 'quasistrata'} of points with the
fibers of $G_F$ of constant dimension. It turns out that T-W-a (Thom and
Whitney-a) stratifications 'near' $F^{-1}(0)$ exist iff the fibers of bundle
$G_F$ are orthogonal to the tangent spaces at the smooth points of the
quasistrata (e. g. when $ l=1$). Also, the latter are the orthogonal
complements over an irreducible component $ S $ of a quasistratum only if $S $
is {\bf universal} for the class of {T-W-a} stratifications, meaning that for
any $\{S_j'\}_j $ in the class, $ \Sing (F) = \cup_j S'_j $, there is a
component $S' $ of an $ S_j' $ with $S\cap S'$ being open and dense in both $S
$ and $ S' $.
  {\bf Results.} We prove that T-W-a stratifications with only universal strata
exist iff all fibers of $G_F$ are the orthogonal complements to the respective
tangent spaces to the quasistrata, and then the partition of $\Sing(F)$ by the
latter yields the coarsest {\it universal T-W-a stratification}.
  The key ingredient is our version of {\bf Sard-type Theorem for singular
spaces} in which a singular point is considered to be noncritical iff
nonsingular points nearby are 'uniformly noncritical' (e. g. for a dominating
map $ F: X \to Z $ meaning that the sum of the absolute values of the $l\times
l$ minors of the Jacobian matrix of $ F $, where $ l = \dim (Z) $, not only
does not vanish but, moreover, is separated from zero by a positive constant).
