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  "body": "\n## Summary\n\nA topological property is a property of topological spaces such that, if a space has it, each [[homeomorphic|05GZ11PWRY]] space also has it.\nExamples are [[compactness|0QPHW703PV]], [[connectedness|0D939CMME7]], [[separability|0GKJ78948V]], [[metrizability|09KDHB82SG]] and the [[Hausdorff property|0MXB4CKHFW]].\n\n## Remarks\n\nTopological properties are used to show that two spaces are not homeomorphic. For example, $[0, 1]$ is compact and $(0, 1)$ is not, so they are not homeomorphic.\nProperties that depend on a metric are often not topological. For example, $(0, 1)$ and $\\mathbb{R}$ are homeomorphic, but only $\\mathbb{R}$ is [[complete|08EWT7J0SC]] and only $(0, 1)$ is bounded.\n\n## Explanations\n\n### L1 human\n\nA topological property is a property that a space keeps when you deform it by a homeomorphism.\nSize and distance are not topological properties, but the number of pieces of a space is one.\n",
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