Linear extension operators for continuous functions on definable sets in the p-adic context

摘要

Let E be a subset of Q_p~n. A linear extension operator is a linear map that sends a function on E to its extension on some superset of E. In this paper, we show that if E is a semi-algebraic or subanalytic subset of Q_p~n, then there is a linear extension operator T : C(E) → C(Q_p~n(cl EE)) such that T ( f ) is semi-algebraic (subanalytic) whenever f is semi-algebraic (subanalytic).