Properties of monotone path-connected sets

Tsar’kov, I. G.; Царьков, Игорь Германович

doi:10.4213/im8995

Известия Российской академии наук. Серия математическая

2021

DOI: 10.4213/im8995

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Properties of monotone path-connected sets

I. G. Tsar’kov¹,

Игорь Германович Царьков

Abstract: Изучаются монотонно линейно связные множества, а также сильно и слабо связные по Менгеру множества. Вводится новое понятие $\varepsilon$-солнечности и устанавливается его связь с понятием солнечности. Доказывается, что ограниченно компактные солнца в $C(Q)$ являются монотонно линейно связными множествами. Библиография: 14 наименований.

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Cited by 11 publications

References 22 publications

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Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces

Царьков¹

2022

Sb. Math.

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Generalized -piecewise functions constructed from given monotone path-connected boundedly compact subsets of the space are studied. They are shown to be monotone path-connected suns. In finite-dimensional polyhedral spaces, luminosity points of sets admitting a lower semicontinuous selection of the metric projection operator are investigated. An example of a non- -connected sun in a four-dimensional polyhedral normed space is constructed. Bibliography: 14 titles.

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Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces

Царьков¹

2022

Sb. Math.

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Approximative and structural properties of sets in asymmetric spaces

Tsar’kov¹,

Царьков

2022

Известия Российской академии наук. Серия математическая

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Изучаются структурно аппроксимативные характеристики приближающих множеств, которые влекут его солнечность. Доказывается, что в конечномерных полиэдральных пространствах всякое строгое солнце является $P$-клеточноподобным и обладает непрерывной $\varepsilon$-выборкой для всех $\varepsilon>0$. В общих несимметричных пространствах изучаются условия, при которых чебышeвские множества являются солнцами. Библиография: 20 наименований.

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Approximative and structural properties of sets in asymmetric spaces

Царьков

2022

Izv. Math.

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Properties of monotone path-connected sets

Cited by 11 publications

References 22 publications

Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces

Solarity and connectedness of sets in the space and in finite-dimensional polyhedral spaces

Approximative and structural properties of sets in asymmetric spaces

Approximative and structural properties of sets in asymmetric spaces

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