  Determining the pairing symmetry of single-layer FeSe on SrTiO$_3$ is the key
to understanding the enhanced pairing mechanism; furthermore, it guides
exploring new superconductors with high transition temperatures
($T_\mathrm{c}$). Despite significant efforts, it remains controversial whether
the symmetry is the sign-preserving $s$- or the sign-changed $s_{\pm}$-wave.
Here, we investigate the pairing symmetry of single-layer FeSe from a
topological point of view. Using low-temperature scanning tunneling
microscopy/spectroscopy, we have systematically characterized the
superconducting states at isolated edges and corners of single-layer FeSe. The
tunneling spectra collected at edges and corners exhibit full gap and
substantial dip, respectively, demonstrating the absence of topologically
non-trivial edge/corner modes. According to the theoretical calculation, these
spectroscopic features are strong evidence for the sign-preserving $s$-wave
pairing.
