Smooth points ofp-adic subanalytic sets

Ap-adic subanalytic set shares with a real subanalytic set the fundamental property that its singular locus is itself subanalytic. Furthermore, given ap-adic subanalytic function ? with domain contained in ? _p ^m , there is an integerL such that for any pointx ₀ ∈ ? _p ^m in a neighborhood of whichf is defined,f has a Taylor approximation up to orderL atx ₀ if, and only if, ? is analytic aroundx ₀. These results extend to thep-adic fields real variables theorems by M. Tamm [21].