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Class 9 Homework-

Let X and Y be compact spaces. Assume further that Y is Hausdorff. Let f:XY be a continuous surjection. Define the equivalence relation  on X by x1x2 iff f(x1)=f(x2). Then g:X/∼→Y given by g(|x|)=f(x) is a well-defined homeomorphism.




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