Indiscreet topology on quotient space

manpreet Best Answer 2 years ago

I'm studying basical topology and I can't figure out something. In a syllabus I read, it is written "Let RRbe a topological space with the euclidian topology. We can define an equivalence relation such that x∼y⇔x−y∈Qx∼y⇔x−y∈Q". Moreover it is said that "the quotient topology on R/∼R/∼ is the indiscreet topology" but I can' figure out how to prove it.

I tried to prove that any subset (except the empty set) of R/∼R/∼ is close but without information about the topology it seems hard.

Can anyone have an hint?

Thanks!