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