Connected T1 space
Definition
A topological space is termed a connected T1 space if it satisfies the following equivalent conditions:
- It is both a connected space and a T1 space.
- The space is connected and the topology on the space either coincides with or is a finer topology than the cofinite topology on the 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
This article describes a property of topological spaces obtained as a conjunction of the following two properties: connected space and T1 space
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Meaning |
|---|---|---|---|---|
| continuum | ||||
| connected Hausdorff space |