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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $X$ is normal when the property that follows holds.\nFor all disjoint [[closed sets|0G5AV9Q4RR]] $A, B \\subseteq X$, there are [[open sets|01ZQQDCERP]] $U$ and $V$ with $A \\subseteq U$, $B \\subseteq V$ and $U \\cap V = \\varnothing$.\n\n## Remarks\n\nNames vary. Some authors call a space T4 when it is normal and [[T1|05GQJXBP3F]]. Such a space is [[regular|0JF9KW2TXB]] and [[Hausdorff|0MXB4CKHFW]].\nEach [[metrizable space is normal|0AD0BZ49DW]], and each [[compact Hausdorff space is normal|0MQQQ5NA2S]].\nA product of two normal spaces need not be normal. The Sorgenfrey plane is an example.\n[[Urysohn's lemma|01EY3VR7ZD]] characterises normal spaces by continuous functions.\n\n## Explanations\n\n### L1 human\n\nIn a normal space, two closed sets that do not meet can be put into two open sets that do not meet.\nThis is a strong condition, but it holds for all metric spaces.\n",
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