Door space: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
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! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions | |||
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| [[Weaker than::discrete space]] || || || || | |||
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===Weaker properties=== | |||
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! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions | |||
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| [[Stronger than::submaximal space]] || || || || {{intermediate notions short|submaximal space|door space}} | |||
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| [[Stronger than::hereditarily irresolvable space]]|| || || || {{intermediate notions short|hereditarily irresolvable space|door space}} | |||
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| [[Stronger than::irresolvable space]] || || || || {{intermediate notions short|irresolvable space|door space}} | |||
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Revision as of 17:58, 28 January 2012
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
A door space is a topological space in which every subset is either open or closed.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| discrete space |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| submaximal space | |FULL LIST, MORE INFO | |||
| hereditarily irresolvable space | |FULL LIST, MORE INFO | |||
| irresolvable space | |FULL LIST, MORE INFO |