  In spite of extensive works on the non-Hermitian topology, correlations
effects remain crucial questions. We hereby analyze correlated non-Hermitian
systems with special emphasis on the one-dimensional point-gap topology.
Specifically, our analysis elucidates that correlations result in reduction of
the topological classification $\mathbb{Z}\times \mathbb{Z} \to \mathbb{Z}$ for
systems of one synthetic dimension with charge $\mathrm{U(1)}$ symmetry and
spin-parity symmetry. Furthermore, we analyze an extended Hatano-Nelson chain
which exhibits striking correlation effects; correlations destroy the skin
effect at the non-interacting level. This fragility of the skin effect against
interactions is consistent with the reduction of the point-gap topology in the
one spatial dimension. The above discoveries shed new light on the topology of
correlated systems and open up new directions of researches on non-Hermitian
topological physics.
