  We present rigorous topological order which emerges in a one-dimensional
spin-orbital model due to the ring topology. Although an exact solution of a
spin-orbital ring with SU(2) spin and XY orbital interactions separates spins
from orbitals by means of a unitary transformation, the spins are not
independent when the ring is closed, but form two half-rings carrying opposite
pseudomomenta. We show that an inverse transformation back to the physical
degrees of freedom entangles the spin half-rings with the orbitals once again.
This surprising correlation arises on changing the topology from an open to a
closed chain, which reduces the degeneracy of the ground-state manifold,
leaving in it only the states in which pseudomomenta compensate each other.
