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  "body": "\n## Definition\n\nA [[topological space|0CNQXVBHCX]] $(X, \\tau)$ is metrizable when there is a [[metric|063W5JMY85]] $d$ on $X$ whose [[metric topology|0A6YRNZB2R]] is $\\tau$.\n\n## Remarks\n\nThe metric is not unique: equivalent metrics give the same topology.\nEach metrizable space is [[Hausdorff|0MXB4CKHFW]] and [[normal|0AD0BZ49DW]].\nAn indiscrete space with at least two points is not metrizable.\nUrysohn's metrization theorem: each [[second-countable|00RE1R4W7N]] [[regular|0JF9KW2TXB]] Hausdorff space is metrizable.\n\n## Explanations\n\n### L1 human\n\nA metrizable space is a topological space where you can measure distances in a way that gives exactly the open sets you already have.\nProperties that hold in all metric spaces then hold in this space.\n",
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