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  "body": "\n## Example\n\nLet $X$ be a set and let $\\tau = \\mathcal{P}(X)$ be the set of all subsets of $X$.\nThen $\\tau$ is a [[topology|0CNQXVBHCX]] on $X$, the discrete topology. The space $(X, \\tau)$ is a discrete space.\n\n## Remarks\n\nEach subset of $X$ is both open and closed. Each point $x$ gives an open set $\\{x\\}$.\nIt is the finest topology on $X$. It is the [[metric topology|0A6YRNZB2R]] of the [[discrete metric|0NA4FK7B8S]].\nEach function from a discrete space to any topological space is [[continuous|0SY9ECQ19Q]].\nA discrete space is [[compact|0QPHW703PV]] if and only if it is finite.\n\n## Explanations\n\n### L1 human\n\nIn the discrete topology, every set is open, so each point is isolated from all other points.\nThe integers $\\mathbb{Z}$, as a subspace of $\\mathbb{R}$, carry the discrete topology.\n",
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