Tagged Questions
1
vote
2answers
84 views
P-adic numbers complete/incomplete
P-adic numbers are complete in one sense and incomplete in another sense. Is it so?
Firstly, does not complete mean connected? I read somewhere that there is not intermediate value theorem for ...
1
vote
1answer
121 views
About $p$-adic Topology on $\mathbb{Z}$
I want some notes about $p$-adic Topology and some properties with proves about $\mathbb{Z}$ with this Topology.
Thank you.
1
vote
1answer
81 views
Why $\mathbb{Z}$ with $p$-adic topology is precompact?
Why $\mathbb{Z}$ (group of integer numbers) with $p$-adic topology is a countable precompact metric group with a linear topology?
Note : Call a topological group $G$ linear (and its topology a linear ...
2
votes
1answer
521 views
Open set = *disjoint* union of open balls?
Recently, i have read the assertion that in $Q_p$, the p-adics, every open set is a disjoint union of open balls. This is not true for a general metric space, see for example How to make open covers ...
6
votes
2answers
330 views
Is the algebraic closure of a $p$-adic field complete
Let $K$ be a finite extension of $\mathbf{Q}_p$, i.e., a $p$-adic field. (Is this standard terminology?)
Why is (or why isn't) an algebraic closure $\overline{K}$ complete?
Maybe this holds more ...
5
votes
2answers
457 views
Why are closed balls in the $p$-adic topology compact?
I was skimming through some of this paper Measurable Dynamics and Simple $p$-adic Polynomials out of curiosity.
A few pages in, the author claims that closed balls are both open and compact sets in ...
4
votes
0answers
171 views
Intersection of nested open sets
Consider a nested sequence $O_1$, $O_2$, $\dots , O_k, \dots $ of open sets in $\mathbb{Q}_p^n$ such that $O_i \setminus O_{i+1}$ has empty interior. Under which conditions do we have
$\bigcap_k O_k$ ...
