  Platforms for creating Majorana quasiparticles rely on superconductivity and
breaking of time-reversal symmetry. By studying continuous deformations to
known trivial states, we find that the relationship between superconducting
pairing and time reversal breaking imposes rigorous bounds on the topology of
the system. Applying these bounds to $s$-wave systems with a Zeeman field, we
conclude that a topological phase transition requires that the Zeeman energy at
least locally exceed the superconducting pairing by the energy gap of the full
Hamiltonian. Our results are independent of the geometry and dimensionality of
the system.
