Ultraconnected space: Difference between revisions
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| [[Stronger than::connected space]] || || || || {{intermediate notions short|connected space|ultraconnected space}} | | [[Stronger than::connected space]] || || || || {{intermediate notions short|connected space|ultraconnected space}} | ||
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| [[Stronger than::normal | | [[Stronger than::normal space]] || || || || | ||
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| [[Stronger than::pseudocompact space]] || || || || | | [[Stronger than::pseudocompact space]] || || || || | ||
Revision as of 17:40, 28 January 2012
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 space | ||||
| pseudocompact space | ||||
| limit point-compact space |