All Questions

Let $\Bbb Q_p$ be a p-adic field and let any element $x$ of $\Bbb Q_p$ be associated with a unique element of $\Bbb Z_p$ via the quotient / equivalence relation $\forall n\in\Bbb Z:p^nx\sim x$ Then in ...

Take the field $\mathbb{Q}$, If we complete it topologically with respect to the Euclidean norm, we get $\mathbb{R}$, then if we complete it algebraically, we get $\mathbb{C}$. On the other hand, the ...

Let $\|\cdot\|_p$ denote the $p$-adic norm on $\mathbb{Q}$. For the whole set of primes $P$ consider the topology which is generated with prebase of open sets $V_{p,\varepsilon}(x) = \{y\in\mathbb{Q} :...

Let $K$ be a discrete valued (with discrete valuation $v$) complete local division ring with ring of valuation $V$. Let $F$ be a compact subset of $V$. Suppose that for all $x\in F$ and for all $y\in ...

Let $p$ be a prime number. Let $n,m \geq 1$ be such that the topological spaces $\mathbb{Q}_p^n$ and $\mathbb{Q}_p^m$ are homeomorphic. Can we conclude $n=m$? For $\mathbb{Z}_p$ it's false: In fact, ...