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## The subspace gives information

Functional Analysis
Papapetros Vaggelis
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### The subspace gives information

Let $\displaystyle{\left(X,||\cdot||\right)}$ be a normed space (real or complex) and $\displaystyle{Y}$

a linear subspace of $\displaystyle{X}$ such that $\displaystyle{\rm{int}(Y)\neq \varnothing}$.

Then, $\displaystyle{X=Y}$.