Let then define an equivalence relation on s.t.
if and only if
So denoting the elements of as
defines a homemorphism.
is continuous since which is the sum of continous functions.
Letting so injective.
Now for s.t.
Since we have so which is in so surjective.
Therefore a bijection.
Not sure how to show continuous?
Is this correct? Any input would be great. Thanks