Door space
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 |