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  "body": "\n## Definition\n\nLet $X$ and $Y$ be [[topological spaces|0CNQXVBHCX]].\nA function $f \\colon X \\to Y$ is an open map when for each [[open set|01ZQQDCERP]] $U$ of $X$, the [[image|0Q3F20XB0A]] $f(U)$ is open in $Y$.\n\n## Remarks\n\nThe [[projections of a product|0PM88Z9W4M]] $X \\times Y \\to X$ are open maps.\nA continuous bijection is a [[homeomorphism|05GZ11PWRY]] if and only if it is an open map.\nThe map $\\mathbb{R} \\to \\mathbb{R}$, $x \\mapsto x^2$, is continuous but not open: the image of $(-1, 1)$ is $[0, 1)$.\n\n## Explanations\n\n### L1 human\n\nAn open map keeps open sets open when you push them forward.\nContinuity is about pulling open sets back, so the two notions are different.\n",
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