  The interplay between symmetry and topology led to the discovery of
symmetry-protected topological phases in Hermitian systems, including
topological insulators and topological superconductors. However, the intrinsic
symmetry-protected topological characteristics of non-Hermitian systems still
await exploration. Here, we investigate experimentally the topological
transition associated with the inversion of non-Hermitian band structures in an
optical lattice. Intriguingly, we demonstrate that the winding number
associated with the symmetry-protected bound state in the continuum is not a
conserved quantity after band inversion. To define a topological invariant, we
propose the skyrmion number given by spawning in momentum space a pseudo-spin
with the polarisation vortex as the in-plane component and the band-index as
the pseudo-spin direction at the origin. This leads to a topological transition
from an antimeron to an meron-like texture through band inversion, while always
conserving the half-charge skyrmion number. We foresee the use of skyrmion
number to explore exotic singularities in various non-Hermitian physical
system.
