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## Main Question or Discussion Point

Hi All,

I've come across a theorem that I'm trying to prove, which states that:

The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete..

To a lesser extent I'm also interested in the H being closed iff G/H Haussdorf.

Thanks!

I've come across a theorem that I'm trying to prove, which states that:

The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete..

To a lesser extent I'm also interested in the H being closed iff G/H Haussdorf.

Thanks!