[[Separation axioms]]
# Normal space

A **normal space** is a [[topological space]] $(X,\mathcal{T})$ such that any two disjoint closed subsets $A,B \sube X$ have disjoint open neighbourhoods $U,V \in \mathcal{T}$, #m/def/topology 
i.e. $A \sube U \in \mathcal{T}$ and $B \sube V \in \mathcal{T}$.
A **$\mathrm{T}_{4}$ space** is one which is both normal and [[Hausdorff space|Hausdorff]]. #m/def/topology 

## Properties

- [[Hausdorff-compact implies normal]]

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