Topic summary
Normal space
In topology and related branches of mathematics, a normal space is a topological space in which any two disjoint closed sets have disjoint open neighborhoods. Such spaces need not be Hausdorff in general. A normal Hausdorff space is called a T4 space. Strengthenings of these concepts are detailed in the article below and include completely normal spaces and perfectly normal spaces, and their Hausdorff variants: T5 spaces and T6 spaces. All these conditions are examples of separation axioms.