Theorem 9.7.1 (Remmert–Stein)B1493CF698A6

Theorem 9.7.1 (Remmert–Stein).B1493CF698A6 Let $X$ be a complex space, let $p\geq 0$ be an integer, and let $A\subset X$ be an analytic subset of dimension at most $p$. Let $Z$ be an analytic subset of $X\setminus A$ all of whose local branches have dimension greater than $p$. Then the closure of $Z$ in $X$ is analytic.