Unionofconvexset

In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset ...

由 J Matoušek 著作 · 1997 · 被引用 21 次 — Abstract. We prove that for any d, k ≥ 1 there are numbers q = q(d,k) and h = h(d,k) such that the following holds: Let K be a family of subsets of the d- ...

2014年11月10日 — I don't think subtraction of convex sets is convex. Let's look at a particular example in 1 dimension of a union of convex sets not being ...

2018年12月8日 — Given A a convex set of Rn such that int(A)≠∅, prove that int(cl(A))=int(A).

由 RL McKinney 著作 · 1966 · 被引用 21 次 — We present here a generalization of property P3 which characterizes closed sets in an arbitrary topological linear space which are the union of two convex ...

In general, union of two convex sets is not convex. To obtain convex sets from union, we can take convex hull of the union. Exercise 1. Draw two convex sets ...

由 JF Lawrence 著作 · 1972 · 被引用 31 次 — ABSTRACT. In this paper it is shown that a set is the union of k convex subsets if and only if every finite subset of it is contained in.

2020年4月26日 — No. Union of two convex sets may not be a convex set . Remember that a line AB joining any two points A, B in a plane is a convex set .

It is the largest convex set contained in both of them. The union of two convex sets need not be convex, but the convex hull of the union is the smallest convex ...