Monotonically normal 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
This is a variation of normality. View other variations of normality
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Definition with symbols
A topological space is termed monotonically normal if there exists an operator from ordered pairs of disjoint closed sets to open sets, such that:
- For any disjoint closed subsets , contains and its closure is disjoint from
- If and with all four sets being closed, and disjoint from , we have:
This is the monotonicity condition. Such an operator is termed a monotone normality operator.
Relation with other properties
This property of topological spaces is hereditary, or subspace-closed. In other words, any subspace (subset with the subspace topology) of a topological space with this property also has this property.
View other subspace-hereditary properties of topological spaces
Any subspace of a monotonically normal space is monotonically normal.