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  "body": "\n## Definition\n\nLet $(X, \\tau_X)$ and $(Y, \\tau_Y)$ be [[topological spaces|0CNQXVBHCX]] and let $f \\colon X \\to Y$ be a function.\nThe function $f$ is continuous when for each [[open set|01ZQQDCERP]] $V \\in \\tau_Y$, the [[preimage|0FGCFY1AZX]] $f^{-1}(V)$ is in $\\tau_X$.\n\n## Remarks\n\nEquivalently, $f$ is continuous if and only if preimages of closed sets are closed, as in [[continuity via closed sets|0B8GPXFSP7]].\nFor metric spaces, this is the same as the epsilon-delta condition, by [[continuity via open sets|0YF82GBTND]].\nA function is continuous if and only if it is [[continuous at each point|07N7W5C29X]].\nConstant maps and identity maps are continuous, and the [[composition of continuous maps is continuous|05NK26G0DR]].\n\n## Explanations\n\n### L1 human\n\nA continuous map does not tear the space apart: the points that go into an open set come from an open set.\nThis definition uses only open sets, so it works in each topological space.\n",
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