ASL STEM

Interval Sign Video

Upload On Thu Oct 23 2014 by ASL STEM

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Definition

Suppose that X is a set having a simple order relation <. Given element a and b of X such that a<b, there are four subsets of X that are called the intervals determined by a and b. They are the following: (a, b)={x|a < x < b}, (a, b]={x|a < x<= b}, [a, b)={x|a <= x < b}, [a, b]={a <= x <= b}. A set of the first type is called an open interval in X, a set of the last type is called a closed interval in X, and sets of the second and third types are called half-open intervals.

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

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> Mathematics

> Field Of Topology

> Interval

+ 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 *

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+ Pointwise Boundedness *

+ Topologically Complete *

+ Baire Space *

+ Compact Open Topology *

+ Compactly Generated *

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+ Evaluation Map *

+ General Position *

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+ Affinely Independent *

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+ Topological Dimension *

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+ Ascoli's Theorem *

+ Box Topology *

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+ Fundamental Thm Of Algebra *

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