Thin Right Triangle Convexity

Abstract

Let F be a family of sets in Rd (always d≥2). A set M⊂Rd 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 thin right triangle is the boundary of a non-degenerate right triangle in R2. The aim of this paper is to introduce and begin investigating the thin right triangle convexity for short trt-convexity, which is obtained when F is the family of all thin right triangles. We investigate the trt-convexity of unbounded sets, convex surfaces and planar geometric graphs.