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.
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