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.
Sources
- 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.4$: Vector spaces