  The classical Jordan curve theorem for digital curves asserts that the Jordan
curve theorem remains valid in the Khalimsky plane. Since the Khalimsky plane
is a quotient space of $\mathbb R^2$ induced by a tiling of squares, it is
natural to ask for which other tilings of the plane it is possible to obtain a
similar result. In this paper we prove a Jordan curve theorem which is valid
for every locally finite tiling of $\mathbb R^2$. As a corollary of our result,
we generalize some classical Jordan curve theorems for grids of points,
including Rosenfeld's theorem.
