Notes:Quotient topology plan

Obviously putting the quotient topology in the page called quotient topology is the way forward, however the order in which to introduce the quotient topology, quotient space and quotient map can be varied. It's also not as if the concepts are even distinct, I have a theory that given one form you actually induce the others. Thus there's really only one definition hiding here.

Map [ilmath]\iff[/ilmath] equivalence relation

It is sufficient to show that given a map we can get an equivalence relation, and given an equivalence relation, we can get a map. This is obviously true.

Thus the set one is certainly true.

Quotient map results from applying the quotient topology

Trivial.

The quotient topology gives rise to a quotient map

Both trivial.