Ultraconnected space
Definition
A topological space is termed an ultraconnected space if it is a non-empty space and an two non-empty disjoint 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 | ||||
| connected space | |FULL LIST, MORE INFO | |||
| normal-minus-Hausdorff space | ||||
| pseudocompact space | ||||
| limit point-compact space |