  We discuss a phase structure of compact QED in four dimensions by considering
the theory as a perturbed topological model. In this scenario we use the
singular configuration with an appropriate regularization, and so obtain the
results similar to the lattice gauge theory due to the effect of topological
objects. In this paper we calculate the thermal pressure of the topological
model by the use of a one-dimensional Coulomb gas approximation, which leads to
a phase structure of full compact QED. Furthermore the critical-line equation
is explicitly evaluated. We also discuss relations between the monopole
condensation in compact QED in four dimensions and the chiral symmetry
restoration in the massive Thirring model in two dimensions.
