Is every point $x \in U$ in an open set $U \subset X$of a normed space $(X,||\cdot||)$ a limit point?
2026-04-09 16:57:18.1775753838
limit point of open sets
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Yes, because for $x \neq 0$ we have $x =\lim (1+\frac 1 n) x$. For $x=0$ take any non-zero vector $y$ in $U$ and write $x$ as the limit of $\frac 1 n y$.