A striking feature of non-Hermitian systems is the presence of two types of topology. One generalizes Hermitian topological phases, and another is intrinsic to non-Hermitian systems, called line-gap topology and point-gap topology. Whereas the bulk-boundary correspondence is a fundamental principle in the former topology, its role in the latter has not been clear yet. In this talk, I argue the bulk-boundary correspondence in the point-gap topology in non-Hermitian systems. After revealing the requirement for point-gap topology in the open boundary conditions, we clarify that the bulk point-gap topology in open boundary conditions can differ from that in periodic boundary conditions. We classify the open boundary (symmetry-protected) point-gap topology entirely and show that the non-trivial open boundary topology results in robust and exotic surface states. I also discuss a universal realization of point-gap topological phases from topological materials.

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