On weakly m-convex sets

Authors

  • H. К. Dakhil Тaras Shevchenko National University of Kiev
  • Yu. B. Zelinskii Institute of Mathematics of the NAS of Ukraine, Kiev
  • B. А. Klishchuk Institute of Mathematics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2017.04.003

Keywords:

1-hull of a family of sets, conjugate set, Grassmann manifold, m-convex set, problem of shadow, weakly m-convex set

Abstract

Some properties of weakly m-convex sets are studied. Various variants of the problem of shadow are investigated. The lower bound for the number of balls that are necessary to create a shadow at a point tangential to sphere S2 in the Euclidean space R3, is obtained.

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References

Zelinskii, Yu. B. (2012). Convexity. Selected topics. Kiev: Institute of Mathematics of the NAS of Ukraine (in Russian).

Zelinskii, Yu. B., Momot, I. V. (2001). On the (n, m) convex sets. Ukr. Math. J., 53, No 3, rpp. 422-427 (in Russian). https://doi.org/10.1023/A:1012352607365

Zelinskii, Yu. B., Gretsky, A. S., Momot, I. V. Some results on generalized convex sets. Classical analysis, Proceedings of 10-th intern. sympos. Poland, 1999, pp. 113-124.

Rohlin, V. A., Fuks, D. B. (1977). Basic Topology Course. Moscow: Nauka (in Russian).

Zelinskii, Yu. B. (2015). The problem of shadow for family of sets. Zbirnyk prats' In-tu matematyky NAN Ukrainy, 12, No 4: 197-204 (in Russian).

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Published

01.07.2024

How to Cite

Dakhil H. К., Zelinskii, Y. B., & Klishchuk B. А. (2024). On weakly m-convex sets . Reports of the National Academy of Sciences of Ukraine, (4), 3–7. https://doi.org/10.15407/dopovidi2017.04.003

Issue

No. 4 (2017): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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