Let then define an equivalence relation on s.t.

if and only if

Show that

So denoting the elements of as

The function

defines a homemorphism.

is continuous since which is the sum of continous functions.

Letting so injective.

Now for s.t.

Then

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