  Topological order is a new type order that beyond Landau's symmetry breaking
theory. The topological entanglement entropy provides a universal quantum
number to characterize the topological order in a system. The topological
entanglement entropy of the BTZ black hole was calculated and found that it
coincides with that for fractional quantum Hall state. So the BTZ black holes
have the same topological order with the fractional quantum Hall state. We
conjecture that black holes in higher dimensions also have topological orders.
Next we want to study the topological order of ordinary spaces which can be
described by spin network states in loop quantum gravity. We advise to bring in
the methods and results in string-net condensation to loop quantum gravity to
solve some difficult problems.
