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Right Quadruple Convexity of Complements

Author

Listed:
  • Xuemei He

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang 050024, China
    Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang 050024, China)

  • Liping Yuan

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Hebei Key Laboratory of Computational Mathematics and Applications, Hebei Normal University, Shijiazhuang 050024, China
    Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang 050024, China)

  • Tudor Zamfirescu

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang 050024, China
    Fachbereich Mathematik, Technische Universität Dortmund, 44221 Dortmund, Germany
    Roumanian Academy, 014700 Bucharest, Romania)

Abstract

Let F be a family of sets in R d (always d ≥ 2 ). A set M ⊂ R d is called F -convex , if for any pair of distinct points x , y ∈ M , there is a set F ∈ F , such that x , y ∈ F and F ⊂ M . A set of four points { w , x , y , z } ⊂ R d is called a rectangular quadruple , if conv { w , x , y , z } is a non-degenerate rectangle. If F is the family of all rectangular quadruples, then we obtain the right quadruple convexity , abbreviated as r q - convexity . In this paper we focus on the r q -convexity of complements, taken in most cases in balls or parallelepipeds.

Suggested Citation

  • Xuemei He & Liping Yuan & Tudor Zamfirescu, 2022. "Right Quadruple Convexity of Complements," Mathematics, MDPI, vol. 11(1), pages 1-6, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:84-:d:1014858
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