Ultraconnected space: Difference between revisions
| Line 1: | Line 1: | ||
==Definition== | ==Definition== | ||
A [[topological space]] is termed an '''ultraconnected space''' if it is a non-empty space and | 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== | ==Relation with other properties== | ||
Revision as of 00:37, 5 January 2017
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 |