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  "body": "\n## Example\n\nA [[continuum|NJQ196M1WR]] $X$ is *chainable* if for every $\\varepsilon \u003e 0$ there is a finite cover of $X$ by open sets $U_1, \\dots, U_n$ of the following kind.\nEach $U_i$ has diameter less than $\\varepsilon$, and $U_i$ meets $U_j$ only when $\\abs{i - j} \\le 1$.\nThe *pseudo-arc* is a nondegenerate chainable continuum in which every subcontinuum is [[indecomposable|56J7DSVAZH]].\nIt can be built in the plane as the intersection of a decreasing sequence of chains of discs.\nEach chain is folded back and forth inside the previous one in a specific crooked way.\nKnaster gave the first such continuum, and Bing proved that any two such continua are homeomorphic.\nThe pseudo-arc is indecomposable, since by its definition every subcontinuum, including the whole space, is indecomposable.\n\n## Remarks\n\nThe pseudo-arc is homogeneous: for any two points there is a homeomorphism of the space onto itself that sends one to the other.\nIt is homeomorphic to each of its nondegenerate subcontinua, as Moise proved.\nThe arc $[0, 1]$ is also chainable and also homeomorphic to its nondegenerate subcontinua, but it is decomposable; this is why the name \"pseudo-arc\" fits.\n\n## Explanations\n\n### L1 human\n\nThe pseudo-arc looks like an arc from far away, since it can be covered by a thin chain of small links.\nUp close it is folded back on itself at every scale, so that no piece of it is a simple arc.\nEvery piece of it is as tangled as the whole, and every piece looks the same as the whole.\n",
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