User:Leigh.Samphier/Todo

P-adic last links

 * : $\S 3.3$ Exploring $\Q_p$, Lemma $3.3.4$
 * P-adic Integers is Metric Completion of Integers


 * : $\S 1.4$ The field of $p$-adic numbers $\Q_p$, Proposition $3.2.12$
 * Definition:P-adic Number

Common
Bold

Let $\struct {R, \norm{\,\cdot\,}}$ be a normed division ring with zero $0_R$ and unity $1_R$.

Let $\struct {R, \norm{\,\cdot\,}}$ be a non-Archimedean normed division ring with zero $0_R$ and unity $1_R$.

Let $d$ be the metric induced by the norm $\norm{\,\cdot\,}$.

Let $\tau$ be the topology induced by the norm $\norm{\,\cdot\,}$.

Let $\norm {\,\cdot\,}_p$ be the $p$-adic norm on the rationals $\Q$ for some prime $p$.

Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Cleanup
Neighborhood in Topological Subspace iff Intersection of Neighborhood and Subspace

Local Compactness in Hausdorff Space

Equivalence of Definitions of Locally Connected Space

Equivalence of Definitions of Locally Path-Connected Space

Equivalence of Definitions of Locally Compact Hausdorff Space

Necessary and Sufficient Condition for Convergent Sequence (Metric Space)

Subspace Topology does not depend on Ambient Space

Definition:Field Norm

Group Inverse Reverses Ordering in Ordered Group

Add Definition:Normed Division Algebra to Norm

 * Definition:Normed Division Algebra

Further Ideas
Definition:Stone Space Stone's Representation Theorem for Boolean Algebras

Definition:Frames & Locales

Nagata-Smirnov Metrization Theorem

Stone-Weierstrass Theorem

Gelfand-Naimark Theorem

Jordan Curve Theorem

Gelfand-Mazur Theorem