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  "body": "\n## Summary\n\nA space is $n$-connected if it is nonempty, path-connected, and its [[homotopy groups|P976WYEFMB]] vanish in degrees $1$ to $n$.\nIt generalises path-connected ($0$-connected) and simply connected ($1$-connected) spaces.\nConnectivity sets the range in which the Hurewicz, Freudenthal and Blakers–Massey theorems apply.\n\n## Explanations\n\n### L1 human\n\nA space is $n$-connected if every sphere of dimension at most $n$ inside it can be shrunk to a point.\nBeing $0$-connected means any two points can be joined by a path.\nBeing $1$-connected means also that every loop can be contracted.\nThe $3$-sphere is $2$-connected: every loop and every small balloon on it can be shrunk.\n",
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