Alexandroff 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 a principal space or Alexandroff space if it satisfies the following equivalent conditions:

• Every point has a unique minimal neighbourhood
• An arbitrary union of open subsets is open
• An arbitrary union of closed subsets is closed

Relation with other properties

Stronger properties

• Trivial space (viz a set with the trivial topology)
• Discrete space

Weaker properties

• Orthocompact space