ASL STEM

Second Countability Axiom Sign Video

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Definition

If a space X has a countable basis for its topology, then X is said to satisfy the second countability axiom, or to be second-countable.

Source: Topology (second edition) by James R. Munkres

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> Mathematics

> Field Of Topology

> Second Countability Axiom

+ Tychonoff Theorem *

+ Interval

+ Subspace *

+ Basis *

+ Topological Space *

+ Finer *

+ Coarser *

+ Discrete Topology *

+ Indiscrete (Trivial) Topology *

+ Metric *

+ Standard Topology *

+ Subbasis *

+ K Topology *

+ Lower Limit Topology *

+ Subspace Topology *

+ The Pasting Lemma *

+ Product Space *

+ Unit Circle *

+ Topology (On A Set) *

+ First Countability Axiom *

+ Standard Bounded Metric *

+ The Sequence Lemma *

+ Total Boundedness *

+ Uniform Limit Theorem *

+ Uniform Metric *

+ Uniform Topology *

+ Unit 2 Sphere *

+ Quoitent Topology *

+ Quotient Map *

+ Open Map *

+ T1 Axiom *

+ Totally Disconnected *

+ Linear Continuum *

+ Punctured Euclidean Space *

+ Unit Sphere *

+ Local Connectedness *

+ Local Path Connectedness *

+ Path Connected *

+ Path Components *

+ Separation *

+ Topological Group *

+ Limit Point Compactness *

+ Fininite Intersection Property *

+ Isolated Point *

+ Lebesgue Number *

+ Lebesgue Number Lemma *

+ Sequentially Compact *

+ The Tube Lemma *

+ Tube *

+ Uniform Continuity Theorem *

+ Second Countable *

+ Completely Normal *

+ One Point Compactification *

- Second Countability Axiom *

+ Sorgenfrey Plane *

+ Urysohn Lemma *

+ Completely Regular *

+ Baire Category Theorem *

+ Imbedding Theorem *

+ M Manifold *

+ Locally Finite *

+ Urysohn Metrization Theorem *

+ Countably Locally Finite *

+ Coutably Locally Discrete *

+ Locally Discrete *

+ Locally Finite Indexed Family *

+ Locally Metrizable *

+ Nagata Smirnov Metrization Thm *

+ Paracompact *

+ Refinement *

+ Smirnov Metrization Theorem *

+ Tietze Extension T Heorem *

+ Point Open Topology *

+ Pointwise Boundedness *

+ Sup Metric *

+ Topologically Complete *

+ Baire Space *

+ Compact Open Topology *

+ Compactly Generated *

+ Empty Interior *

+ Evaluation Map *

+ General Position *

+ Topology Of Compact Convergence *

+ Affinely Independent *

+ Geometrically Independent *

+ Locally M Euclidean *

+ Topological Dimension *

+ Unit Ball (B^N) *

+ Uniform Convergence *

+ Intermediate Value Theorem

+ Hairy Ball Theorem *

+ Local Compactness *

+ Partition Of Unity *

+ Quoitent Space *

+ Uniform Continuity *

+ Diffeomorphism *

+ Cauchy Integral Formula *

+ Fundamental Thm Of Algebra *

* video needed

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