Using low-temperature scanning tunneling microscopy (STM), we studied the vortex states of single-layer FeSe film on SrTiO3 (100) substrate, and the local behaviors of superconductivity at sample boundaries. We clearly observed multiple discrete Caroli-de Gennes-Matricon (CdGM) states in the vortex core, and quantitative analysis shows their energies well follow the formula: E = {mu}{Delta}^2/E_F, where {mu} is a half integer and {Delta} is the mean superconducting gap over the Fermi surface. Meanwhile, a fully gapped spectrum without states near zero bias is observed at [110](Fe) oriented boundary of 1 ML and 2 ML FeSe films, and atomic step edge of 1 ML FeSe. Accompanied with theoretical calculations, our results indicate a s-wave pairing without sign-change in the high-TC FeSe_SrTiO3 superconductor.
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