  A primary motivation for studying topological matter regards the protection
of topological order from its environment. In this work, we study a topological
emitter array coupled to an electromagnetic environment. The photon-emitter
coupling produces nonlocal interactions between emitters. Using periodic
boundary conditions for all ranges of environment-induced interactions, chiral
symmetry inherent to the emitter array is preserved and protects the
topological phase. A topological phase transition occurs at a critical
photon-emitter coupling which is related to the energy spectrum width of the
emitter array. It produces a band touching with parabolic dispersion, distinct
to the linear one without considering the environment. Interestingly, the
critical point nontrivially changes dissipation rates of edge states, yielding
dissipative topological phase transition. In the protected topological phase,
edge states suffer from environment-induced dissipation for weak photon-emitter
coupling. However, strong coupling leads to dissipationless edge states. Our
work presents a way to study topological criticality in open quantum systems.
