Talk:Differentiation in Fréchet spaces

Merge into Gateaux derivative
These articles describe the same concept. — Preceding unsigned comment added by 128.120.104.8 (talk) 20:04, 29 August 2014 (UTC)
 * See Talk:Gâteaux derivative Shhhnotsoloud (talk) 10:14, 12 April 2017 (UTC)

U is an open set of X. X and Y are Frechet spaces, and in particular X and Y are closed to addition. F is a function U to Y. The formal definition of the derivative uses F(u+tv). However, I see no reason that u + tv is in U, and hence F may be undefined on u + tv. If the limit exists then there is a neighborhood where the addition makes sense and one is taking the limit over t and v such that u+tv is in U? I'm confused.
 * Question regarding typing