User:Leigh.Samphier/Todo

P-adic last links

 * : $\S 1.2$ Normed fields, Proposition 1.17
 * Equivalent Norms are both Non-Archimedean or both Archimedean


 * : $\S 2.3$ Topology, Proposition 2.3.6
 * Topological Properties of Non-Archimedean Division Rings

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Add definition of Definition:Topology induced by Division Ring Norm

Add Corollary to Equivalent Norms are both Non-Archimedean or both Archimedean that the p-adic Norm and usual Euclidean Norm are not equivalent - yield different topologies. Add to Definition:P-adic Norm and remove refactor.

Add theorem that p-adic and q-adic Norms are not equivalent

Closed ball is disjoint union of open Balls - Problem 50

 * Closed ball $B(0,1)^-$ is disjoint union of open Balls - Problem 50

Open ball is disjoint union of open Balls - Problem 50

 * Open ball $B(0,1)$ is disjoint union of open Balls - Problem 50

The 'Sphere' is disjoint union of open Balls - Problem 51

 * The 'Sphere' $B(0,1)^- \setminus B(0,1)$ is disjoint union of open Balls - Problem 51

Connected component containing x is singleton x - Proposition 2.3.8

 * Is totally disconnected

Create second proof to P-adic Norm not Complete on Rational Numbers

 * Using Hensel's Lemma/First Form

Create third proof to P-adic Norm not Complete on Rational Numbers

 * $\Q_p$ is uncountable, $\Q$ is countable.

Add Definition:Normed Division Algebra to Norm

 * Definition:Normed Division Algebra

Replaced Pages
Leigh.Samphier/Sandbox/Norm Refactor/Normed Division Algebra replaces Definition:Normed Division Algebra

New Pages
Leigh.Samphier/Sandbox/Norm Refactor/Norm/Division Algebra becomes Definition:Norm/Division Algebra