# Definition:Convex Set (Vector Space)/Definition 1

## Definition

Let $\Bbb F \in \set {\R, \C}$.

Let $V$ be a vector space over $\Bbb F$.

Let $C \subseteq V$.

We say that $C$ is convex if and only if:

$t x + \paren {1 - t} y \in C$

for each $x, y \in C$ and $t \in \closedint 0 1$.