Connected T1 space

Definition

A topological space is termed a connected T1 space if it satisfies the following equivalent conditions:

1. It is both a connected space and a T1 space.
2. 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