Talk:Function vanishing at infinity

"In many cases $C_0(X)$ determines $X$, see e.g. Banach–Stone theorem" — Yes, but in Banach-Stone theorem $C_0(X)$ is treated as a Banach space (rather than Banach algebra; in the latter case the claim is almost trivial). Boris Tsirelson (talk) 22:37, 10 January 2018 (CET)