Smooth points ofp-adic subanalytic sets
Tóm tắt
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 ƒ with domain contained in ℤ
, there is an integerL such that for any pointx
0 ∈ ℤ
in a neighborhood of whichf is defined,f has a Taylor approximation up to orderL atx
0 if, and only if, ƒ is analytic aroundx
0. These results extend to thep-adic fields real variables theorems by M. Tamm [21].
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