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Concept
Normal space
Summary
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space. These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T5 spaces, and perfectly normal Hausdorff spaces, or T6 spaces.
Definitions
A topological space X is a normal space if, given any disjoint closed sets E and F, there are neighbourhoods U of E and V of F that are also disjoint. More intuitively, this condition says that E and F can be separated by neighbourhoods.
A T4 space is a T1 space X that is normal; this is equivalent to X being normal and Hausdorff.
A completely normal space, or , is a topological space X such that every subspace of X with subspace topology is a normal space. It turns out that X is completely normal if and only if every two separated s
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