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 Post subject: Vector spacePosted: Mon Oct 24, 2016 8:40 pm
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Joined: Mon Nov 09, 2015 1:52 pm
Posts: 423
Let $\displaystyle{A}$ be a non-empty set and $\displaystyle{\mathcal{F}}$ be a non-empty collection

of $\displaystyle{1-1}$ and onto functions $\displaystyle{f:A\to \mathbb{R}^n}$ such that : if

$\displaystyle{f\,,g\in\mathcal{F}}$ then $\displaystyle{f\circ g^{-1}:\mathbb{R}^n\to \mathbb{R}^n}$

is $\displaystyle{\mathbb{R}}$ - linear isomorphism.

Prove that the set $\displaystyle{A}$ is a vector space (uniquely defined) and each $\displaystyle{f\in\mathcal{F}}$

is $\displaystyle{\mathbb{R}}$ - linear isomorphism.

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