In Euclidean space, a region is a convex set if the following is true. For any two points inside the region, a straight line segment can be drawn. If every point on that segment is inside the …

Sep 26, 2024 · A convex set is a subset of a vector space that has a specific property: for any two points within the set, the line segment connecting them lies entirely within the set. In simple …

Informally, a convex set is a set of points such that for any pair of points in the set, all the points between them (that is, on the line segment that joins them) are members of the set as well. …

Nov 23, 2023 · $\set {t x + \paren {1 - t} y: t \in \closedint 0 1}$ is called the (straight) line segment joining $x$ and $y$ . A convex set can thus be described as a set containing all straight line …

Mar 27, 2022 · Convex Subset of Natural Numbers. Let $A \subseteq \N$ be a subset of the set of natural numbers. $A$ is defined as being convex (in $\N$) if and only if: $\forall x, y, z \in \N: …

Mar 5, 2025 · A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex …

In geometry, a set of points is convex if it contains every line segment between two points in the set. Equivalently, a convex set or a convex region is a set that intersects every line in a line …

Dec 10, 2018 · A convex set is a set of points such that, given any two points A, B in that set, the line AB joining them lies entirely within that set. Intuitively, this means that the set is connected …

Basic Properties of Convex Sets 3.1 Convex Sets Convex sets play a very important role in geometry. In this chapter, we state some of the “classics” of convex affinegeometry: …

In mathematics, a convex body in - dimensional Euclidean space is a compact convex set with non- empty interior. Some authors do not require a non-empty interior, merely that the set is …

A convex set is a set which contains all of the line segments whose endpoints are in it. Formally, a set C RN is said to be convex if for any x1 and x2 in C the point x1 + (1 )x2 2 C for any 2 [0; 1]. …

Oct 23, 2017 · A set containing with two arbitrary points all points of the segment connecting these points. The intersection of any family of convex sets is itself a convex set. The smallest …

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 conta...

In a vector space, a set is said to be convex if every point on the line segment connecting any two points in the set is also in the set. Thus, for a convex set C the following holds true: Let x 1 , x …

A Danzer set, in an n-dimensional Euclidean space, is a set of points in the space that has a non-empty intersection with every convex body whose n-dimensional volume is one. The whole …

In this section, we introduce one of the most important ideas in the theory of optimization, that of a convex set. We discuss other ideas which stem from the basic de nition, and in particular, the …