Topospaces, The Topology Wiki (pre-pre-alpha)

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From Topospaces

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

Contents 1 Definition 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties

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