Denote by the family of isometry classes of compact n-dimensional Alexandrov spaces with curvature , and the eigenvalue of the Laplacian on . We prove the continuity of with respect to the GromovHausdorff topology for each , and moreover that the spectral topology introduced by Kasue-Kumura ,  coincides with the Gromov-Hausdorff topology on .
Takashi SHIOYA. "Convergence of Alexandrov spaces and spectrum of Laplacian." J. Math. Soc. Japan 53 (1) 1 - 15, January, 2001. https://doi.org/10.2969/jmsj/05310001