# general topology – \$R/Q\$ is compact

$$mathbb R/mathbb Q$$ is known to be compact, where topology on $$mathbb R$$ is Euclid topology, and define $$a~b$$ is equivalent to $$a-binmathbb Q$$, topology on $$mathbb R/mathbb Q$$ is given by quotient topology.

Then, I want to prove $$mathbb R/mathbb Q$$ is compact.
I know in general, ‘Let $$G$$ be a topology group. and $$H$$ is dense in $$G$$, then, $$G/H$$ is trivial topology’.

But I want to prove the titled statement without using the fact above.