The phase diagram of the superfluid phase coupled to spin singlet (S=0) and isospin triplet (T=1) states in infinite nuclear matter is analyzed within the nonrelativistic Skyrme model. We use an approach that allows a unified and consistent treatment of the particle-hole and particle-particle channels. The gap equation is solved for the full range of accessible densities, isospin asymmetries, and temperatures. The characteristic features of each of the components Tz=0, ±1 are emphasized. The search for signatures of a BCS-BEC crossover yields negative results within the scheme proposed.Instituto de Física La Plata