Lower Bound of the Upper Topological Limit of a Sequence of Subspaces

Aram V. Arutyunov

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Aram V. Arutyunov

V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Peoples' Friendship University, 117997 Moscow, Russia

arutyunov@cs.msu.ru

Keywords

Sequence of subspaces
upper topological limit
lower bound

Mathematics Subject Classification

46B20

Suggested citation

A. V. Arutyunov. “Lower Bound of the Upper Topological Limit of a Sequence of Subspaces.” Journal of Convex Analysis 27 (2020), No. 1, 49–51.