  We prove that any compact semi-algebraic set is homeomorphic to the solution
space of some art gallery problem. Previous works have established similar
universality theorems, but holding only up to homotopy equivalence, rather than
homeomorphism, and prior to this work, the existence of art galleries even for
simple spaces such as the M\"obius strip or the three-holed torus were unknown.
Our construction relies on an elegant and versatile gadget to copy guard
positions with minimal overhead. It is simpler than previous constructions,
consisting of a single rectangular room with convex slits cut out from the
edges. We show that both the orientable and non-orientable surfaces of genus
$n$ admit galleries with only $O(n)$ vertices.
