# Do elements having any $p$ power roots form a open subset in a perfectoid field

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?