General topology

Dense set

In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation). Formally, is dense in if the smallest closed subset of containing is itself. The density of a topological space is the least cardinality of a dense subset of (Wikipedia).

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From playlist Course 6: Introduction to Analysis (Fall 2017)

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From playlist Advanced Calculus

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From playlist Sets (Discrete Math)

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From playlist Set Theory

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From playlist Course 6: Introduction to Analysis

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From playlist Topology

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From playlist Set Theory

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From playlist Set Theory

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From playlist LAFF - Week 9

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From playlist Mathematics

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The Green-Tao theorem and a relative Szemeredi theorem - Yufei Zhao

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From playlist Mathematics

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From playlist Mathematics

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From playlist Mathematics

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From playlist Mathematics

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From playlist ML Projects

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From playlist Logic and Foundations

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From playlist Axiomatic Set Theory

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From playlist Talks and Tutorials

Related pages

Topological space | Metric space | Baire category theorem | Continuous linear extension | Countable set | Diophantine approximation | Closure (topology) | Separable space | Hyperconnected space | Topology | Isolated point | Nowhere dense set | Intersection (set theory) | Continuous function | Topological vector space | Disjoint sets | Domain of a function | Unit interval | Complement (set theory) | Rational number | Baire space | Hausdorff space | Polynomial function | Neighbourhood (mathematics) | Dense-in-itself | Transitive relation | Open set | Cardinal number | Connected space | Mathematics | Surjective function | Union (set theory) | Real number | Resolvable space | Embedding | Meagre set | Cartesian product | Subset | Interior (topology) | Limit of a sequence | Compact space | Trivial topology | Compactification (mathematics) | Complex number | Irrational number | Subspace topology | Cardinality | Uniform convergence | Image (mathematics) | Closed set | Densely defined operator