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Let $K$ be a perfectoid field, if $K$ has positive characterestic then every $a \in K$ has any $p$ power roots i.e $a=x^{p^n}$ have solutions for any positive integer $n$.

However, in characteristic zero case there maybe elements do not admit $p$ power roots. Anyway, are them form a opensubset in $K$? If not, do they at least contain a open subset?

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