
Journal of Convex Analysis 27 (2020), No. 1, 049051 Copyright Heldermann Verlag 2020 Lower Bound of the Upper Topological Limit of a Sequence of Subspaces Aram V. Arutyunov V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Peoples' Friendship University, 117997 Moscow, Russia arutyunov@cs.msu.ru A new short proof of the following assertion is presented. Given an integer k and a sequence of closed linear subspaces of a Banach space, assume that the codimension of each subspace does not exceed k. Then the upper topological limit of this sequence contains a closed linear subspace with codimension not exceeding k. Keywords: Sequence of subspaces, upper topological limit, lower bound. MSC: 46B20. [ Fulltextpdf (62 KB)] for subscribers only. 