Totally disconnected group

Summary

A totally disconnected group is a topological group whose underlying space is totally disconnected. Equivalently, its identity component is the trivial subgroup. Profinite groups, $p$-adic groups and discrete groups are examples. For a totally disconnected locally compact group, van Dantzig's theorem gives a base of compact open subgroups at the identity. This is the starting point of the structure theory of such groups.