# Connected Hausdorff space

From Topospaces

*This article describes a property of topological spaces obtained as a conjunction of the following two properties:* connectedness and Hausdorffness

This is a variation of connectedness. View other variations of connectedness

This is a variation of Hausdorffness. View other variations of Hausdorffness

## Definition

A **connected Hausdorff space** is a topological space which is both connected and Hausdorff.

## Facts

There do exist countably infinite connected Hausdorff spaces.