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Journal of Convex Analysis 27 (2020), No. 1, 049--051
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

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.

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