ASL STEM

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Definition

Suppose that T and T' are two topologies on a given set X. If T' includes T, we say that T' is finer than T; if T' properly contains T, we say that T' is strictly finer than T. Other terminology is sometimes used for this concept. If T' contains T, some mathematicians would say that T' is larger than T.

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

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> Mathematics

> Field Of Topology

> Finer

+ Tychonoff Theorem *

+ Topological Space *

+ Discrete Topology *

+ Indiscrete (Trivial) Topology *

+ Standard Topology *

+ Lower Limit Topology *

+ Product Topology *

+ Homeomorphism *

+ Limit Point *

+ Hausdorff Space *

+ Neighborhood *

+ Order Topology *

+ Subspace Topology *

+ The Pasting Lemma *

+ Product Space *

+ Unit Circle *

+ Topology (On A Set) *

+ Bounded (Set) *

+ Metric Topology *

+ 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 *

+ Totally Disconnected *

+ Linear Continuum *

+ Punctured Euclidean Space *

+ Unit Sphere *

+ Local Connectedness *

+ Local Path Connectedness *

+ Path Connected *

+ Path Components *

+ Topological Group *

+ Limit Point Compactness *

+ Fininite Intersection Property *

+ Isolated Point *

+ Lebesgue Number *

+ Lebesgue Number Lemma *

+ Sequentially Compact *

+ The Tube Lemma *

+ Uniform Continuity Theorem *

+ Second Countable *

+ Completely Normal *

+ Directed Set *

+ First Countable *

+ Lindelof Space *

+ One Point Compactification *

+ Second Countability Axiom *

+ Sorgenfrey Plane *

+ Urysohn Lemma *

+ Completely Regular *

+ Baire Category Theorem *

+ Imbedding Theorem *

+ Locally Finite *

+ Urysohn Metrization Theorem *

+ Countably Locally Finite *

+ Coutably Locally Discrete *

+ Locally Discrete *

+ Locally Finite Indexed Family *

+ Locally Metrizable *

+ Nagata Smirnov Metrization Thm *

+ Paracompact *

+ Smirnov Metrization Theorem *

+ Tietze Extension T Heorem *

+ Cauchy Sequence *

+ Equicontinuity *

+ Peano Space *

+ Point Open Topology *

+ Pointwise Boundedness *

+ 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 *

+ Connectedness *

+ Ascoli's Theorem *

+ Box Topology *

+ Compactification *

+ 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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