Connected normal space

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This article describes a property of topological spaces obtained as a conjunction of the following two properties: connectedness and normality

This is a variation of normality. View other variations of normality
This is a variation of connectedness. View other variations of connectedness

Definition

A connected normal space is a topological space which is both connected and normal.

Facts

  • Any connected normal space with at least two points has cardinality at least that of the continuum. This follows by considering an Uryoshn function that separates the two points, and observing that connectedness forces the Urysohn function to be surjective. For full proof, refer: Connected Urysohn implies uncountable