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  "body": "\n## Summary\n\nA Polish space is a [[separable|0Z2P41SVDP]] [[topological space|0CQHFPGJ45]] whose topology comes from a [[complete metric|0BY52JW6NK]].\nExamples are the real line, $\\R^n$, the [[Cantor set|0BXNDZFQME]], the [[Baire space|P2WS16HKD7]] and every separable Banach space.\nPolish spaces are the natural setting of [[descriptive set theory|TF8HMVXKYC]] and of much of probability theory.\nThe name honours the Polish topologists and logicians, such as Sierpiński and Kuratowski, who first studied these spaces in depth.\n\n## Explanations\n\n### L1 human\n\nA Polish space is a space where limits of Cauchy sequences exist and where a countable set of points comes close to every point.\nThe real line is the model case: the rationals are dense, and Cauchy sequences converge.\nThe topology matters, not the chosen metric: the open interval $(0, 1)$ is Polish, even though its usual metric is not complete, because it is homeomorphic to the real line.\n",
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