Abstract
We show some topological properties of semianalytic subsets of rigid analytic varieties: curve selection lemma, the closure\(\bar S\) of a semianalytic subsetS is semianalytic,\(f(\bar S) = \overline {f(S)}\) for every quasi-compact morphismf. As an application we show that a morphismf: X → Y of rigid analytic varieties is open at a pointx εX if and only if SpecO X,x → SpecO Y,f(x) is surjective.
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