  We study the correspondence between boundary spectrum of non-chiral
topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and
the entanglement spectrum in the bulk of gapped topological orders on a closed
manifold. The closed manifold is bipartitioned into two subsystems, one of
which has the same topology as $\mathcal{M}$. Specifically, we focus on the
case of generalized string-net models and discuss the cases where $\mathcal{M}$
is a disk or a cylinder. When $\mathcal{M}$ has the topology of a cylinder,
different combinations of boundary conditions of the cylinder will correspond
to different entanglement cuts on the torus. When both boundaries are charge
(smooth) boundaries, the entanglement spectrum can be identified with the
boundary excitation distribution spectrum at infinite temperature and constant
fugacities. Examples of toric code, $\mathbb{Z}_N$ theories, and the simple
non-abelian case of doubled Fibonacci are demonstrated.
