User:Leigh.Samphier/Todo

Common
Help:LaTeX Editing

Bold

$\begin{cases} 1 & : i = j \\ 0 & : i \ne j \end{cases}$

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.

Topology

 * : $\S 4$ Connectedness and Compactness, Proposition $4.1$

Missing Pages
Intersection is Largest Subset/Set of Sets

Equivalence of Definitions of Convergent Sequence in Topology

Strongly Locally Compact Hausdorff Space is Locally Compact & Definition:Strongly Locally Compact Space

Strongly Locally Compact Space may not be Locally Compact

Definition:Locally Metrizable Space

Basis of Countable Finite Complement Topology consists of Countably Infinite Sets

Equivalence of Definitions of Disconnected Set

Equivalence of Definitions of Quaternion Conjugate

Intersection of Compact Sets is Compact

Union of Compact Sets is Compact

P-Norm is Norm & P-Seminorm is Seminorm

P-Product Metrics are Topologically Equivalent

P-adic Valuation is Additive

Path Component is Closed

Quotient Topology is Topology

Definition:Quotient Topology/Definition 2

Triangle Inequality/Quaternions

Definition:Discontinuous (Topology)

Definition:Open Neighborhood (Metric Space)

Definition:Neighborhood of Real Point

Definition:Open Unit Ball

Definition:P-Sequence Norm

Definition:Point of Topological Space

Cleanup
Real and Imaginary Part Projections are Continuous

Definition:Euclidean Metric

Definition:Open Neighborhood/Real Analysis

Special:WantedPages
Nagata-Smirnov Metrization Theorem, Stephen Willard - General Topology

Smirnov Metrization Theorem

Stone-Weierstrass Theorem, Stephen Willard - General Topology

Stone-Cech Compactification, Stephen Willard - General Topology

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

Definition:Frames & Locales

Gelfand-Naimark Theorem

Jordan Curve Theorem

Gelfand-Mazur Theorem

Fix Product Space Issues
Leigh.Samphier/Sandbox/Existence of Completely Normal Space whose Product Space is Not Normal

Leigh.Samphier/Sandbox/Topological Product of Compact Spaces/Finite Product

Leigh.Samphier/Sandbox/Finite Product of Weakly Locally Compact Spaces is Weakly Locally Compact

Leigh.Samphier/Sandbox/Finite Product of Sigma-Compact Spaces is Sigma-Compact

Leigh.Samphier/Sandbox/Countable Product of Sequentially Compact Spaces is Sequentially Compact

Leigh.Samphier/Sandbox/Uncountable Product of Sequentially Compact Spaces is not always Sequentially Compact

Leigh.Samphier/Sandbox/Infinite Product of Weakly Locally Compact Spaces is not always Weakly Locally Compact

Leigh.Samphier/Sandbox/Infinite Product of Sigma-Compact Spaces is not always Sigma-Compact

Leigh.Samphier/Sandbox/Product of Countably Compact Spaces is not always Countably Compact

Leigh.Samphier/Sandbox/Product of Lindelöf Spaces is not always Lindelöf

Leigh.Samphier/Sandbox/Finite Product Space is Connected iff Factors are Connected/General Case

Leigh.Samphier/Sandbox/Products of Products are Homeomorphic to Collapsed Products

Leigh.Samphier/Sandbox/Uncountable Product of First-Countable Spaces is not always First-Countable

Leigh.Samphier/Sandbox/Uncountable Product of Second-Countable Spaces is not always Second-Countable

Leigh.Samphier/Sandbox/Uncountable Product of Separable Spaces is not always Separable

Leigh.Samphier/Sandbox/Product of Paracompact Spaces is not always Paracompact

Leigh.Samphier/Sandbox/Product of Metacompact Spaces is not always Metacompact

[[Leigh.Samphier/Sandbox/Paracompactness is Preserved under Projections

Leigh.Samphier/Sandbox/Tychonoff's Theorem

Leigh.Samphier/Sandbox/Tychonoff's Theorem Without Choice

Leigh.Samphier/Sandbox/Paracompactness is Preserved under Projections

Leigh.Samphier/Sandbox/Box Topology may not form Categorical Product in the Category of Topological Spaces

Leigh.Samphier/Sandbox/Product Space is Product in Category of Topological Spaces