  Let $Y$ be a Gromov-Hausdorff limit of complete Riemannian n-manifolds with
Ricci curvature bounded from below.
  A point in $Y$ is called $k$-regular, if its tangent is unique and is
isometric to an $k$-dimensional Euclidean space.
  By \cite{B5}, there is $k>0$ such that the set of all $k$-regular point
$\mathcal{R}_k$ has a full renormalized measure.
  An open problem is if $\mathcal{R}_l=\emptyset$ for all $l<k$? The main
result in this paper asserts that if $\mathcal{R}_1\ne \emptyset$, then $Y$ is
a one dimensional topological manifold. Our result improves the Handa's result
\cite{Honda} that under the assumption that $1\leq \mathrm{dim}_H(Y)<2$.
