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Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series

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Topology of directional convexity

https://doi.org/10.29235/1561-2430-2020-56-4-408-410

Abstract

Herein, we have proven a Fink – Wood conjecture that if Oʹ is the closure of some orientation set O, then a set is a directed O-halfspace if and only if it is a directed Oʹ-halfspace.

About the Author

V. G. Naidenko
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus

Vladimir G. Naidenko – Ph. D. (Physics and Mathematics), Leading Researcher

11, Surganov Str., 220072, Minsk



References

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2. Fink E., Wood D. (2004) Restricted-Orientation Convexity. Series: Monographs in Theoretical Computer Science. An EATCS Series. Berlin, New York: Springer-Verlag, 2004. 120 p. https://doi.org/10.1007/978-3-642-18849-7

3. Naidenko V. G. Partial convexity. Mathematical Notes, 2004, vol. 75, no. 1/2, pp. 202–212. https://doi.org/10.1023/b:matn.0000015036.94515.c0

4. Rockafellar R. T. Convex Analysis. Princeton (New Jersey), Princeton University Press, 1970. 467 p.

5. Gorokhovik V. V., Gorokhovik S. Ya. Criterion of global epiLipschitzness of sets. Vestsі Natsyianal’nai akademіі navuk Belarusі. Seryia fіzіka-matematychnykh navuk = Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics series, 1995, no. 1, pp. 118–120 (in Russian).


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ISSN 1561-2430 (Print)
ISSN 2524-2415 (Online)