General topology Connectedness Concept
Connected space
Summary
A topological space is connected when it is not the union of two disjoint nonempty open sets. A connected space is in one piece.
Where this leads
24 pages build on this one.
- Riemann domain over C^n
- Long line
- Jordan–Brouwer separation theorem
- Holomorphic functions on compact complex manifolds are constant
- Knaster–Kuratowski fan
- Lakes of Wada
- Schoenflies theorem
- Jordan curve theorem
- Hauptvermutung
- Connected sum
- Radó's theorem on triangulation of surfaces
- Universal covering group
- Algebraic dimension
- Annulus theorem
- Continuum
- Sierpiński space
- Sierpiński carpet
- Kneser's theorem on solution sets
- Hahn–Mazurkiewicz theorem
- Alexander horned sphere
- Jordan curve theorem for polygons
- Genus
- Reinhardt domain
- Menger sponge
Further reading
- Web https://en.wikipedia.org/wiki/Connected_space, lead section
About this page
| Tag | 0V032VWTHD |
|---|---|
| URI | m2://0V032VWTHD |
| Aliases | connectedness |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54D05 |
| Specializes | Topological space |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge not_instance_of in: at least one non-example (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
Special cases
Used by
- Riemann domain over C^n
- Long line
- Jordan–Brouwer separation theorem
- Holomorphic functions on compact complex manifolds are constant
- Knaster–Kuratowski fan
- Lakes of Wada
- Jordan curve theorem
- Connected sum
- Universal covering group
- Algebraic dimension
- Continuum
- Sierpiński space
- Sierpiński carpet
- Hahn–Mazurkiewicz theorem
- Jordan curve theorem for polygons
- Genus
- Reinhardt domain
- Menger sponge