User:Leigh.Samphier/Todo

Closed ball is disjoint union of open Balls - Problem 50

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

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

 * The 'Sphere' $B(0,1)^-\B(0,1)$ 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.

Tidy

 * Quotient of Cauchy Sequences is Metric Completion


 * Quotient Ring of Cauchy Sequences is Normed Division Ring


 * Combination Theorem for Sequences/Normed Division Ring/Inverse Rule

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

Refactor Definition:Absolute Value

 * Replace $\struct {\mathbb K, \size{\,\cdot\,}}$ with $\struct {\mathbb K, \norm{\,\cdot\,}}$ in Definition:Valued Field pages.


 * Replace Definition:Abstract Absolute Value, Definition:Absolute Value/Norm Theory and Definition:Absolute Value/Field with appropriate use of Definition:Valued Field