It is shown that convex hypersurfaces in Hilbert space forms have corresponding lower bounds on Alexandrov curvature. This extends earlier work of Buyalo, Alexander, Kapovitch, and Petrunin for convex hypersurfaces in Riemannian manifolds of finite dimension.

In the present paper, the Liouville theorem and the finite dimension theorem of polynomial growth harmonic functions are proved on Alexandrov spaces with nonnegative Ricci curvature in the sense of Sturm, Lott-Villani and Kuwae-Shioya.

In this paper, we investigate functorial relations between Alexandrov fuzzy topologies and upper approximation operators in complete residuated lattices. We present some examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07, 54A40

We examine the geometry of subspace homogeneous probability measures in terms 2-Wasserstein metric on space all Hilbert spaces functions. show that, appropriate spaces, geodesics joining stay and, as a result, themselves form nonpositive curvature sense A. D. Alexandrov.