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The purpose of this paper is to prove that the conventional state space for the power system is topologically equivalent to the new "local equilibrium state space" introduced by Zaborszky et al.  for emergency control in the large-scale interconnected power system. In , it was shown that there is a one-to-one mapping from the conventional to the new space. This paper proves that this mapping is in fact a homeomorphism (i.e. bijective, continuous, and has continuous inverse), and hence strengthens a usefulness of the "local equilibrium state space."