Good evening.
Yes, I know my title is very unimaginative, but I was not able to find a way to summarize my question.
I have a school assignment that must be written as an article, and my topic is about functional analysis. The "actual math" is pretty much done, but I am struggling to find references about two seemingly basic functional analysis facts:
The topological vector space of test functions is separable.
Tensor products of single-variable smooth compactly-supported real functions span a dense subspace of the topological vector space of smooth compactly-supported functions.
I already know how to prove both, but since these seem very much like known results, I would rather cite some reference. Would you happen to know of any?
Thank you.