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( 6 months ago )

Indiscreet topology on quotient space

Course Queries Syllabus Queries
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Jadav Payeng


( 6 months 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 xyxyQx∼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?


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