What is Frechet Space? Is a Banach a Frechet space? If not, why? If yes, how do we prove it? According to Wikipedia,
Frechet spaces are locally convex topological space that is complete with respect to translation-invariant metric.
It also says that:
They are generalizations of Banach spaces (normed vector spaces that are complete with respect to the metric induced by the norm).
So I am guessing that Frechet spaces are Banach Spaces. But how do we prove it?