  Motivated by the theory of correspondence functors, we introduce the notion
of {\em germ} in a finite poset, and the notion of {\em germ extension} of a
poset. We show that any finite poset admits a largest germ extension called its
{\em germ closure}. We say that a subset $U$ of a finite lattice $T$ is {\em
germ extensible} in $T$ if the germ closure of $U$ naturally embeds in $T$. We
show that any for any subset $S$ of a finite lattice $T$, there is a unique
germ extensible subset $U$ of $T$ such that $U\subseteq S\subseteq
\overline{G}(U)$, where $\overline{G}(U)\subseteq T$ is the embedding of the
germ closure of $U$.
