New Criteria for the Existence of a Continuous ε-Selection

Царьков, Игорь Германович

doi:10.1134/s0001434618110147

Math Notes

2018

DOI: 10.1134/s0001434618110147

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New Criteria for the Existence of a Continuous ε-Selection

Игорь Германович Царьков

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Cited by 8 publications

References 11 publications

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Approximative properties of sets and continuous selections

Tsar’kov¹

2020

Sb. Math.

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Sets admitting a continuous selection of the operators of best and near-best approximation are studied. Michael’s classical continuous selection theorem is extended to the case of a lower semicontinuous metric projection in finite-dimensional spaces (with no a priori convexity conditions on its values). Sufficient conditions on the metric projection implying the solarity of the corresponding set are put forward in finite-dimensional polyhedral spaces. Available results for suns are employed to establish the existence of continuous selections of the relative (with respect to ) Chebyshev near-centre map and of the sets of relative (with respect to ) near-Chebyshev points in certain classical spaces. Bibliography: 30 titles.

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Approximative properties of sets and continuous selections

Tsar’kov¹

2020

Sb. Math.

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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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Properties of Monotone Connected Sets

Tsar’kov

2021

Math Notes

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New Criteria for the Existence of a Continuous ε-Selection

Cited by 8 publications

References 11 publications

Approximative properties of sets and continuous selections

Approximative properties of sets and continuous selections

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

Properties of Monotone Connected Sets

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