An expanding system of linearly closed sets

In this note it is proved that if an open cube in the Euclidean space Rⁿ can be represented in the form of the union of an expanding system of linearly closed sets, then at least one of them has an interior point. This result is applied to the investigation of real-valued functions of several variables.Translated from Matematicheskie Zametki, Vol. 19, No. 1, pp. 67–84, January, 1976.