Ultraconnected space
Definition
A topological space is termed an ultraconnected space if it is a non-empty space and any two non-empty closed subsets have non-empty intersection.
Relation with other properties
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| path-connected space | ultraconnected implies path-connected | |FULL LIST, MORE INFO | ||
| connected space | |FULL LIST, MORE INFO | |||
| normal space | ultraconnected implies normal | |FULL LIST, MORE INFO | ||
| pseudocompact space | |FULL LIST, MORE INFO | |||
| limit point-compact space | |FULL LIST, MORE INFO |