Shadow's problem

Authors

  • Yu.B. Zelinskii
  • I.Yu. Vyhovs’ka
  • M.V. Stefanchuk

DOI:

https://doi.org/10.15407/dopovidi2015.05.015

Keywords:

m-convex set, m-hull of a set, m-semiconvex hull of a set, m-semiconvex set, problem of shadow, simplex

Abstract

The problem of shadow is solved. It is equivalent to the condition for a point to be in the generalized convex hull of a family of compact sets.

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References

Zelinskii Yu.B. Multivalued mappings in the analysis, Kyiv: Naukova Dumka, 1993 (in Russian).

Zelinskii Yu.B. Convexity. Selected topics. Proc. of Institute of Mathematics NASU, Kyiv, 2012, Vol. 92 (in Russian).

Khudaiberganov G. On uniformly polynomially convex hull of the union of balls, Moscow, 1982, Manuscript Dep. VINITI 02.21.1982, No 1772–85 (in Russian).

Schaefer H. Topological vector spaces. – Graduate Texts inMathematics, Vol. 3, New York, Berlin: Springer, 1971. https://doi.org/10.1007/978-1-4684-9928-5

Spanier E. Algebraic topology, New York, Berlin: Springer, 1981. https://doi.org/10.1007/978-1-4684-9322-1

Zelinskii Yu.B. Ukr. Math. J., 2002, 54, No 1: 149–153. https://doi.org/10.1023/A:1019753822066

Leichtweiss K. Konvexe Mengen, Berlin, New York: Springer, 1980. https://doi.org/10.1007/978-3-642-95335-4

Published

03.02.2025

How to Cite

Zelinskii, Y., Vyhovs’ka, I., & Stefanchuk, M. (2025). Shadow’s problem . Reports of the National Academy of Sciences of Ukraine, (5), 15–20. https://doi.org/10.15407/dopovidi2015.05.015