Scientific publications

А.В. Иванов, О.В. Фомкина.

О порядке метрической аппроксимации максимальных сцепленных систем и емкостных размерностях

// Труды КарНЦ РАН. No 7. Сер. Математическое моделирование и информационные технологии. 2019. C. 5-14

A.V. Ivanov, O.V. Fomkina. On the order of metric approximation of maximal linked systems and capacitarian dimensions // Transactions of Karelian Research Centre of Russian Academy of Science. No 7. Mathematical Modeling and Information Technologies. 2019. Pp. 5-14

Keywords: capacitarian dimension; order of metric approximation; superextension

It is shown that in any metric compact space X there exists a countable closed subset F whose upper capacitarian dimension dimBF is equal to any preassigned non-negative number not exceeding the upper capacitarian dimension of X. A similar assertion is proved for the upper order of the metric approximation ord(ξ) of maximal linked systems. Namely, for any number a satisfying the inequalities 0 a dimBX there exists ξ ∈ λ(X) for which ord(ξ) = a and supp(ξ) = X.

URL: http://journals.krc.karelia.ru/index.php/mathem/article/view/1034

DOI: 10.17076/mat1034

Indexed at RSCI

Last modified: July 1, 2019