$\textbf{Separation of a normed space by its dual space}$
Let $X$ be a normed space and $x_1, x_2\in X$, $x_1\neq x_2$. Then there exists $x^*\in X^*$ such that $x^*(x_1)\neq x^*(x_2)$.
$\textbf{Separation of a normed space by its dual space}$
Let $X$ be a normed space and $x_1, x_2\in X$, $x_1\neq x_2$. Then there exists $x^*\in X^*$ such that $x^*(x_1)\neq x^*(x_2)$.
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๐๐๐ฉ๐๐ซ๐๐ญ๐ข๐จ๐งย ๐จ๐ย ๐ย ๐ง๐จ๐ซ๐ฆ๐๐ย ๐ฌ๐ฉ๐๐๐ย ๐๐ฒย ๐ข๐ญ๐ฌย ๐๐ฎ๐๐ฅย ๐ฌ๐ฉ๐๐๐
Let ๐ be a normed space and ๐ฅโ,๐ฅโโ๐, ๐ฅโโ ๐ฅโ. Then there exists ๐ฅ*โ๐* such that ๐ฅ*(๐ฅโ)โ ๐ฅ*(๐ฅโ).