Talk:Gâteaux variation

Are we assuming that Y is a Hausdorff space? Otherwise the limit might not be unique.

Indeed, according to our "Topological vector space" article, it is generally not Hausdorff. On the other hand, according to Wikipedia, "Some authors (e.g., Rudin) require the topology on X to be T0; it then follows that the space is Hausdorff, and even T3½".

P.S. Do not forget to sign your remarks by four tildas ("~~~~"). --Boris Tsirelson 13:26, 28 May 2012 (CEST)