Open subgroup
= Open subgroup
An open <subgroup> is also closed, since its complement is the union of its other open <cosets>. Conversely a closed subgroup need not be open, as $\mathbb Z\subset\mathbb R$ shows.
= Open subgroup
An open <subgroup> is also closed, since its complement is the union of its other open <cosets>. Conversely a closed subgroup need not be open, as $\mathbb Z\subset\mathbb R$ shows.