Let $F$ be a local field with a non-Archimedean absolute value. Then the Schwartz space, or the collection of Schwartz-Bruhat functions, consists of the functions from $F$ to $\mathbb C$ that are locally constant and have compact support.
It is often either denoted $C_c^\infty(F)$ or $\mathcal S(F)$.
Wikidata ID: Q1369621