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  "body": "\n## Summary\n\nThe inductive dimensions of a topological space are defined by induction from the dimension of boundaries.\nA space has dimension at most $n$ when points, or closed sets, have small neighbourhoods whose boundaries have dimension at most $n - 1$.\nThere are two versions, the small inductive dimension $\\operatorname{ind}$ and the large inductive dimension $\\operatorname{Ind}$.\nFor separable metric spaces both agree with the [[Lebesgue covering dimension|A3W7RGXXK9]].\n\n## Explanations\n\n### L1 human\n\nA solid ball in space can be cut out from its surroundings by its surface, which is two-dimensional.\nA disc in the plane is cut out by a circle, which is one-dimensional, and an interval on a line is cut out by two points, which are zero-dimensional.\nThe inductive dimension turns this into a definition: the dimension of a space is one more than the dimension of the walls one needs to cut out small pieces.\nThe empty set has dimension $-1$ to start the induction.\n",
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