摘要
Let Y be a Gromov-Hausdorff limit of complete Riemannian nmanifolds with Ricci curvature bounded from below. A point in Y is called k-regular, if its tangent is unique and is isometric to a k-dimensional Euclidean space. By Cheeger-Colding and Colding-Naber, there is k 〉 0 such that the set of all k-regular point ：Rk has a full renormalized measure. An open problem is if Rl = 0 for all l 〈 k？ The main result in this paper asserts that if R1 ≠ 0, then Y is a one-dimensional topological manifold. Our result improves Honda＇s result that under the assumption that 1 ≤ dimH（Y） 〈 2.
Let Y be a Gromov-Hausdorff limit of complete Riemannian nmanifolds with Ricci curvature bounded from below. A point in Y is called k-regular, if its tangent is unique and is isometric to a k-dimensional Euclidean space. By Cheeger-Colding and Colding-Naber, there is k 〉 0 such that the set of all k-regular point ：Rk has a full renormalized measure. An open problem is if Rl = 0 for all l 〈 k？ The main result in this paper asserts that if R1 ≠ 0, then Y is a one-dimensional topological manifold. Our result improves Honda＇s result that under the assumption that 1 ≤ dimH（Y） 〈 2.
