General topology Metric spaces Concept
Open ball
Summary
An open ball in a metric space is the set of all points at distance strictly less than a given radius from a given centre. Open balls are the basic open sets of a metric space.
Where this leads
17 pages build on this one.
- Removable singularities for harmonic functions
- Zaremba's punctured ball
- Hardy–Littlewood maximal function
- Doubling measure
- Harmonic function on a ball
- Lebesgue point
- Sub-mean value property
- Lebesgue spine
- Koebe's theorem on the mean value property
- Poisson integral formula
- Least harmonic majorant
- Lebesgue differentiation theorem
- Green's function of the ball
- Lebesgue's density theorem
- Bôcher's theorem
- Expansion in spherical harmonics
- Hartogs lemma for subharmonic functions
Further reading
- Web https://en.wikipedia.org/wiki/Ball_(mathematics), In general metric spaces
About this page
| Tag | 0YE5868HZB |
|---|---|
| URI | m2://0YE5868HZB |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54E35 |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge instance_of in: at least two examples (1 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)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Zaremba's punctured ball
- Hardy–Littlewood maximal function
- Doubling measure
- Harmonic function on a ball
- Lebesgue point
- Lebesgue spine
- Poisson integral formula
- Lebesgue differentiation theorem
- Green's function of the ball
- Lebesgue's density theorem
- Expansion in spherical harmonics