General topology Basic notions: open sets, neighbourhoods, bases Concept
Dense set
Summary
A dense subset of a topological space is a subset whose closure is the whole space. Each nonempty open set meets a dense set.
Where this leads
37 pages build on this one.
- Stone–Weierstrass theorem
- Continuous additive functions are linear
- Namioka--Phelps
- Compactification
- L2 convergence of Fourier series
- Rational map
- Oppenheim conjecture
- Particular point topology
- Poincaré classification of circle homeomorphisms
- Excluded point topology
- Continuous functional calculus
- Pompeiu derivative
- Density of simple functions in Lp
- Müntz–Szász theorem
- Topological transitivity
- Multiresolution analysis
- Approximation of a kernel by degenerate kernels
- Minimal set
- Universal approximation theorem
- Separable Banach space
- Goldstine theorem
- Density of trigonometric polynomials in continuous functions
- Compactness of integral operators
- Density of the graph of a discontinuous additive function
- Completion of a normed space
- Commutative Gelfand–Naimark theorem
- Fourier basis of L2 of the circle
- Jentzsch's theorem on positive kernels
- Residual set
- Bishop–Phelps theorem
- Cardinal function
- Devaney chaos
- Noncommutative geometry
- Peixoto's theorem
- Basel problem via Fourier series
- Densely defined operator
- Continuous and residual spectrum
Further reading
- Web https://en.wikipedia.org/wiki/Dense_set, lead section
About this page
| Tag | 0BSJSX7ME2 |
|---|---|
| URI | m2://0BSJSX7ME2 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54A05 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Used by
- Stone–Weierstrass theorem
- Continuous additive functions are linear
- Compactification
- Rational map
- Oppenheim conjecture
- Particular point topology
- Poincaré classification of circle homeomorphisms
- Pompeiu derivative
- Density of simple functions in Lp
- Müntz–Szász theorem
- Topological transitivity
- Multiresolution analysis
- Minimal set
- Universal approximation theorem
- Separable Banach space
- Goldstine theorem
- Density of the graph of a discontinuous additive function
- Completion of a normed space
- Residual set
- Bishop–Phelps theorem
- Cardinal function
- Devaney chaos
- Peixoto's theorem
- Densely defined operator
- Continuous and residual spectrum