Category:Definitions/Convex Sets (Vector Spaces)

This category contains definitions related to Convex Sets (Vector Spaces) in the context of Vector Spaces.
Related results can be found in Category:Convex Sets (Vector Spaces).

Definition 1

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 $t \in \closedint 0 1$.

Definition 2

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

$t C + \paren {1 - t} C \subseteq C$

for each $t \in \closedint 0 1$, where $t C + \paren {1 - t} C$ denotes a linear combination of subsets.