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 | every subset is open |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| submaximal space | every subset is locally closed | |FULL LIST, MORE INFO | ||
| hereditarily irresolvable space | every non-empty subspace is an irresolvable space | |FULL LIST, MORE INFO | ||
| irresolvable space | not a resolvable space, i.e., cannot be expressed as a union of disjoint dense subsets | |FULL LIST, MORE INFO |