## Basic calculus on topological fields

Let $K$ be a a topological field (I am mainly interested in the cases when K is either an ordered field or a valued field, e.g. $K = \mathbb Q$ or $\mathbb Q_p$). 1) Let $f: K^n \to K$ be a function such that its differential $Df$ is constant $0$. Is $f$ constant on … Read more

## Locally compact vector space over a finite field

In the wikipedia article titled “topological vector space”, there is a line saying the following. “Let K be a locally compact topological field, for example to real or complex numbers. A topological vector space over K is locally compact if and only if it is finite-dimensional, that is, isomorphic to Kn for some natural number … Read more

## A characterization of nuclear functionals in terms of continuity with respect to some special topologies on B(X)B(X)?

I think, nuclear functionals on the space of operators B(X) (on a Banach space X) must have a characterization in terms of some special continuity. I would be grateful if somebody could help me with the following hypothesis. First, a nuclear functional on B(X) (where X is a Banach space) is a linear functional u:B(X)→C … Read more