Leigh.Samphier/Sandbox

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RED

$p$-adic Numbers

Continuing Svetlana Katok Book

Leigh.Samphier/Sandbox/P-adic Expansion Representative of P-adic Number is Unique

Leigh.Samphier/Sandbox/Equivalence Class in P-adic Numbers Contains Unique P-adic Expansion

Every P-adic Number is Limit of P-adic Expansion

P-adic Number is Limit of Unique P-adic Expansion - Complete the uniqueness

Leigh.Samphier/Sandbox/Set of P-adic Units is Unit Sphere

Leigh.Samphier/Sandbox/Characterization of Rational P-adic Units

Leigh.Samphier/Sandbox/P-adic Expansion of P-adic Units

Matroids

Loops and Parallel Elements

To be completed.

Properties of Independent Sets and Bases

Leigh.Samphier/Sandbox/Matroid satisfies Base Axiom

Leigh.Samphier/Sandbox/Alternative Axiomatization of Matroid

Topology

Fix Product Space Issues

Leigh.Samphier/Sandbox/Product Local Basis Induced from Factor Spaces Local Bases

Leigh.Samphier/Sandbox/Countable Product of First-Countable Spaces is First-Countable

Leigh.Samphier/Sandbox/Countable Product of Separable Spaces is Separable

Leigh.Samphier/Sandbox/Factor Spaces are T4 if Product Space is T4

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

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

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

Leigh.Samphier/Sandbox/Function to Product Space is Continuous iff Composition with Projections are Continuous

Leigh.Samphier/Sandbox/Metric is Continuous

Leigh.Samphier/Sandbox/Paracompactness is Preserved under Projections

Leigh.Samphier/Sandbox/Points in Product Spaces are Near Open Sets

Leigh.Samphier/Sandbox/Product of Hausdorff Factor Spaces is Hausdorff

Leigh.Samphier/Sandbox/Product of Hausdorff Factor Spaces is Hausdorff/General Result

Leigh.Samphier/Sandbox/Product Space is Completely Hausdorff iff Factor Spaces are Completely Hausdorff

Leigh.Samphier/Sandbox/Product Space is T2 iff Factor Spaces are T2

Leigh.Samphier/Sandbox/Product Space is T3 1/2 iff Factor Spaces are T3 1/2

Leigh.Samphier/Sandbox/Product Space is T3 iff Factor Spaces are T3

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

Leigh.Samphier/Sandbox/Subspace of Product Space Homeomorphic to Factor Space

Leigh.Samphier/Sandbox/Topological Product with Singleton

Leigh.Samphier/Sandbox/Tychonoff's Theorem

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

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

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