Hello,
Prop 11.3. Let G be a topological group.
- If G is $T_1$ then G is Hausdorff
- If G is not $T_1$, let H be the closure of ${e}$. Then H is a normal subgroup, and if G/H is given the quotient topology, G/H is a Hausdorff topological group.
Proof omitted.
The author then says that it's easy to see that borel measurable functions on G are constant on the cosets of H. Why is this?
References: GB Folland - Real Analysis, Modern techniques and their applications, 2nd ed, chapter 11
