  We have simulated the pure gauge compact QED with fixed boundary conditions,
on lattices from $6^4$ to $16^4$. We argue that a lattice with this fixed
boundary imposition corresponds actually to a lattice with spherical topology.
We have found the presence of a phase transition without any trace of
discontinuity. Moreover, the specific heat and the Binder cumulant are
qualitatively consistent with a second order phase transition. The implications
of this observation on the nature of the compact lattice QED are discussed.
