Wednesday, 24 July 2019

calculus - Homeomorphism between two sets

I am to prove that there is no homeomorphism between (a,b) and [a,b)



It is defined that function is bijective, continuous, and inverse continuous.



How can I derive a contradiction assuming that there exists a homeomorphism between two sets?



One approach that I take is if f is continuous map [a,b) to (a,b), then f1((a,b)) must be open set, but [a,b) is not open.



I think this way is more of like set theory rather than using definition of continuity and I doubt this completes proof or not.

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