Linearly orderable 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 topological space is termed linearly orderable if it occurs as the underlying topological space of a linearly ordered space (viz it can be obtained by giving the order topology to a linearly ordered set).

Relation with other properties

Stronger properties

• Well-orderable space

Weaker properties

• Monotonically normal space
• Hereditarily normal space
• Normal space
• Regular space
• Hausdorff space