Definition:Convex Set (Vector Space)/Line Segment

From ProofWiki
Jump to navigation Jump to search

Definition

Let $V$ be a vector space over $\R$ or $\C$.

Let $x, y \in V$.


The set:

$\set {t x + \paren {1 - t} y: t \in \closedint 0 1}$

is called the (straight) line segment joining $x$ and $y$.


A convex set can thus be described as a set containing all straight line segments between its elements.


Sources