Right Quadruple Convexity of Complements

Xuemei He, Liping Yuan () and Tudor Zamfirescu
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Xuemei He: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
Liping Yuan: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
Tudor Zamfirescu: School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China

Mathematics, 2022, vol. 11, issue 1, 1-6

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.

Keywords: rectangular quadruple; rq-convexity; complements (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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