Space in which the connected components coincide with the quasicomponents
Definition
A space in which the connected components coincide with the quasicomponents is a topological space satisfying the following equivalent conditions:
- Each quasicomponent is connected with the subspace topology.
- Each connected component is a quasicomponent.
- Each quasicomponent is a connected component.
- The connected components and quasicomponents coincide.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| connected space | Space in which all connected components are open|FULL LIST, MORE INFO | |||
| space with finitely many connected components | Space in which all connected components are open|FULL LIST, MORE INFO | |||
| locally connected space | Space in which all connected components are open|FULL LIST, MORE INFO | |||
| space in which all connected components are open | |FULL LIST, MORE INFO |