Let be X a topological space and we suppose that E and F are homeomorphic though a

rjawbreakerca 2022-07-12 Answered
Let be X a topological space and we suppose that E and F are homeomorphic though a map f from F to E. So I ask to me if E is open/closed when F is open/closed but unfortunatley I was not able to prove or to disprove this so that I thought to put a specific question where I ask some clarification: in particular if the result is generally false I'd like to know if it can be true we additional hypotesis, e.g. Hausdorff separability, First Countability, Metric Topology, etc....
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Answers (1)

thatuglygirlyu
Answered 2022-07-13 Author has 14 answers
Consider E = ( 0 , 1 ) and F = R .
Obviously, E , F R . It is quite easy to show that F and E are homeomorphic.
F is closed and open. But E is not closed.
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