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)

The concept of function vanishing at infinity is mentioned in the Banach–Stone theorem article but this does not seem particularly important point to make here. I suppose it's about reconstructing the space from the maximal ideals of the algebra, and then the functions that vanish at infinity form an ideal which does not correspond to a point of the space. Richard Pinch (talk) 08:38, 11 January 2018 (CET)