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  "body": "\n## Summary\n\nA totally disconnected group is a [[topological group|92700QAB5Y]] whose underlying space is [[totally disconnected|0RJSBR9GW1]].\nEquivalently, its identity component is the trivial subgroup.\nProfinite groups, $p$-adic groups and discrete groups are examples.\nFor a totally disconnected locally compact group, van Dantzig's theorem gives a base of compact open subgroups at the identity.\nThis is the starting point of the structure theory of such groups.\n\n## Explanations\n\n### L1 human\n\nA totally disconnected group has no connected pieces except single points.\nAny two distinct elements can be separated, so the group looks like dust rather than like a curve or a surface.\nThe $p$-adic integers are the main example.\nTwo $p$-adic integers are close when their difference is divisible by a high power of $p$, and the space falls apart into small separate balls.\nEvery group with the discrete topology is also totally disconnected.\n",
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