Characterization of the interior of a convex set

My inquiry is the following: allow $K$ be a convex embeded in $\mathbb{R}^n$ and also $x$ a component of the inside of $K$. Can I attest that there exist $z_1,...,z_n \in K$ linearly independent and also $\lambda_1,....,\lambda_n > 0$ such that:. \begin{equation} x = \displaystyle \sum_{p=1}^n \lambda_p z_p \quad ??? \end{equation} If this declaration holds true, exists a person that can offer me an evidence? Thanks significantly and also farewell!

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2022-07-25 20:42:46
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