General topology Separation axioms Concept
Hausdorff space
Summary
A Hausdorff space is a topological space in which any two distinct points have disjoint open neighbourhoods. It is the most used separation axiom, and it makes limits of sequences unique.
Where this leads
66 pages build on this one.
- Stone–Weierstrass theorem
- Moore space
- Urysohn space
- L2 convergence of Fourier series
- Filter limit
- Michael selection theorem
- Stone space
- Summation in topological groups
- Space of functions vanishing at infinity
- Fort space
- Kolmogorov's normability criterion
- Continuous functional calculus
- Hausdorff topological group
- Quotient of a topological group
- Monad in nonstandard topology
- Dieudonné's theorem on paracompact Hausdorff spaces
- Borel–Moore homology
- Haar's uniqueness theorem
- Gleason's theorem on projective compact spaces
- Stein space
- Tychonoff plank
- Uniform algebra
- Riesz–Markov–Kakutani representation theorem
- Dowker space
- Line with two origins
- Homotopy group with coefficients
- Manifold with corners
- Arens–Fort space
- Approximation of a kernel by degenerate kernels
- Net
- Radon measure
- Compactly generated space
- Urysohn metrization theorem
- Continuum
- Kolmogorov criterion for best approximation
- Chebyshev system
- Homology manifold
- Banach analytic space
- Nagata–Smirnov metrization theorem
- Existence and uniqueness of Haar measure
- Density of trigonometric polynomials in continuous functions
- Compactness of integral operators
- Stone–Čech compactification
- Sober space
- Commutative Gelfand–Naimark theorem
- Fourier basis of L2 of the circle
- Surface
- Jentzsch's theorem on positive kernels
- Modular function
- Kneser's theorem on solution sets
- Complex manifold
- Hahn–Mazurkiewicz theorem
- Banach–Stone theorem
- Complex analytic space
- Bing metrization theorem
- Noncommutative geometry
- Moore plane
- Étale fundamental group
- Basel problem via Fourier series
- Profinite group
- Convergence along an ultrafilter
- Choquet capacity
- Manifold with boundary
- 3-manifold
- Topological manifold
- Finite-dimensional Hausdorff vector topologies are Euclidean
Further reading
- Web https://en.wikipedia.org/wiki/Hausdorff_space, lead section
About this page
| Tag | 0S1FJ8VEX9 |
|---|---|
| URI | m2://0S1FJ8VEX9 |
| Aliases | t2-space, separated-space |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54D10 |
| Specializes | T1 space |
| 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)
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What links here
Definitions
Used by
- Stone–Weierstrass theorem
- Moore space
- Urysohn space
- Filter limit
- Michael selection theorem
- Stone space
- Summation in topological groups
- Space of functions vanishing at infinity
- Fort space
- Kolmogorov's normability criterion
- Hausdorff topological group
- Quotient of a topological group
- Monad in nonstandard topology
- Dieudonné's theorem on paracompact Hausdorff spaces
- Borel–Moore homology
- Haar's uniqueness theorem
- Gleason's theorem on projective compact spaces
- Stein space
- Tychonoff plank
- Uniform algebra
- Riesz–Markov–Kakutani representation theorem
- Dowker space
- Line with two origins
- Manifold with corners
- Arens–Fort space
- Net
- Radon measure
- Compactly generated space
- Urysohn metrization theorem
- Continuum
- Kolmogorov criterion for best approximation
- Chebyshev system
- Homology manifold
- Banach analytic space
- Nagata–Smirnov metrization theorem
- Stone–Čech compactification
- Sober space
- Surface
- Complex manifold
- Hahn–Mazurkiewicz theorem
- Banach–Stone theorem
- Complex analytic space
- Bing metrization theorem
- Moore plane
- Profinite group
- Convergence along an ultrafilter
- Choquet capacity
- Manifold with boundary
- 3-manifold
- Topological manifold
- Finite-dimensional Hausdorff vector topologies are Euclidean