- See also
- Notes
- References
In mathematics, a topological space 
is said to be ultraconnected if no pair of nonempty closed sets of is disjoint. Equivalently, a space is ultraconnected if and only if the closures of two distinct points always have non trivial intersection. Hence, no 
space with more than 1 point is ultraconnected.[1]
All ultraconnected spaces are path-connected (but not necessarily arc connected[1]), normal, limit point compact, and pseudocompact.
See also
- Hyperconnected space
Notes
1. ^1 Steen and Seeback, Sect. 4
References
- {{PlanetMath attribution|id=5814|title=Ultraconnected space}}
- Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology. Springer-Verlag, New York, 1978. Reprinted by Dover Publications, New York, 1995. {{ISBN|0-486-68735-X}} (Dover edition).
1 : Properties of topological spaces
- SPAD S.G
- Spad s vii
- SPAD S.XI
- SPAD S.XII
- SPAD S.XIV
- SPAD S.XVI
- SPAD XI
- SPAD XII
- SPAD XIV
- SPAD XVI
- Spaehkreuzer 1938
- Spaehpanzer Luchs
- Spaelotis
- Spaelotis cineraria
- Spaelotis clandestina
- Spaelotis crinigera
- Spaelotis eremata
- Spaelotis infuscata
- Spaelotis pectinata
- Spaelotis ravida
- Spaelotis stictica
- Spaelsau (sheep)
- Spaen
- Spaetburgunder
- Spaete Ranfoliza