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  "body": "\n## Definition\n\nLet $(X, \\tau)$ be a [[topological space|0CNQXVBHCX]].\nA subset $U$ of $X$ is open in $X$ when $U \\in \\tau$.\nA subset of a [[metric space|063W5JMY85]] is open when it is open for the [[metric topology|0A6YRNZB2R]].\n\n## Remarks\n\nIn a metric space $(X, d)$, a set $U$ is open if and only if for each $x \\in U$ there is $\\varepsilon \u003e 0$ with $B(x, \\varepsilon) \\subseteq U$. This is the statement [[open sets of a metric space|0A26X79RTB]].\nIn $\\mathbb{R}$, each open interval $(a, b)$ is open, but $[0, 1)$ is not open: no ball about $0$ lies in $[0, 1)$.\nThe empty set and $X$ are always open.\n\n## Explanations\n\n### L1 human\n\nIn a metric space, an open set has no edge points. From each of its points, you can move a little in any direction and stay in the set.\nThe interval $(0, 1)$ is open, because each point has some room on both sides.\n",
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