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  "body": "\n## Summary\n\nA Dowker space is a [[normal|0NSR9V8TED]] Hausdorff space that is not countably paracompact.\nEquivalently, it is a normal Hausdorff space $X$ whose product $X \\times [0, 1]$ with the unit interval is not normal.\nSuch spaces show that normality is not preserved by products, even with a compact metric factor.\nMary Ellen Rudin constructed a Dowker space in ZFC.\n\n## Explanations\n\n### L1 human\n\nNormality is a separation property: two disjoint closed sets can be put inside disjoint open sets.\nOne might expect that multiplying a normal space by the plain interval $[0, 1]$ keeps it normal.\nA Dowker space is a normal space for which this fails.\nEvery metrizable space and every [[paracompact|8R29G6NG9Q]] Hausdorff space is normal and countably paracompact, so none of them is a Dowker space.\nKnown Dowker spaces are hard to build, which is why they count as exotic.\n",
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