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## Main Question or Discussion Point

What is difference between subgroup and closed subgroup of the group? It is confusing to me because every group is closed.

In a book Lie groups, Lie algebras and representations by Brian C. Hall is written

"The condition that ##G## is closed subgroup, as opposed to merely a subgroup, should be regarded as technicality, in the most of interesting subgroups of ##GL(n,\mathbb{C})## have this property."

In a book Lie groups, Lie algebras and representations by Brian C. Hall is written

"The condition that ##G## is closed subgroup, as opposed to merely a subgroup, should be regarded as technicality, in the most of interesting subgroups of ##GL(n,\mathbb{C})## have this property."