Definition:Convex Set (Vector Space)/Definition 2

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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:

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

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


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