  Emergent gravity is based on the Darboux theorem or the Moser lemma in
symplectic geometry stating that the electromagnetic force can always be
eliminated by a local coordinate transformation as far as U(1) gauge theory is
defined on a spacetime with symplectic structure. In this approach, the
spacetime geometry is defined by U(1) gauge fields on noncommutative (NC)
spacetime. Accordingly the topology of spacetime is determined by the topology
of NC U(1) gauge fields. We show that the topology change of spacetime is ample
in emergent gravity and the subsequent resolution of spacetime singularity is
possible in NC spacetime. Therefore the emergent gravity approach provides a
well-defined mechanism for the topology change of spacetime which does not
suffer any spacetime singularity in sharp contrast to general relativity.
