  Non-Hermiticity leads to distinctive topological phenomena absent in
Hermitian systems. However, connection between such intrinsic non-Hermitian
topology and Hermitian topology has remained largely elusive. Here, considering
the bulk and boundary as an environment and system, we demonstrate that
anomalous boundary states in Hermitian topological insulators exhibit
non-Hermitian topology. We study the self-energy capturing the particle
exchange between the bulk and boundary, and demonstrate that it detects
Hermitian topology in the bulk and induces non-Hermitian topology at the
boundary. As an illustrative example, we show the non-Hermitian topology and
concomitant skin effect inherently embedded within chiral edge states of Chern
insulators. We also find the emergence of hinge states within effective
non-Hermitian Hamiltonians at surfaces of three-dimensional topological
insulators. Furthermore, we comprehensively classify our correspondence across
all the tenfold symmetry classes of topological insulators and superconductors.
Our work uncovers a hidden connection between Hermitian and non-Hermitian
topology, and provides an approach to identifying non-Hermitian topology in
quantum matter.
