# Category:Convex Sets (Vector Spaces)

This category contains results about Convex Sets (Vector Spaces) in the context of Vector Spaces.
Definitions specific to this category can be found in Definitions/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.

## Subcategories

This category has the following 9 subcategories, out of 9 total.

## Pages in category "Convex Sets (Vector Spaces)"

The following 29 pages are in this category, out of 29 total.