Discussion
Which of the following sets are homeomorphic ?
Answer: B
The homeomorphic pair is square and ellipse.
The boundary of a square and an ellipse are both simple closed curves. Radial projection from the centre gives a homeomorphism between them, so each is homeomorphic to the circle.
A parabola is homeomorphic to R, which is not compact, so it cannot match the compact square or ellipse. A hyperbola has two separate branches, so it is disconnected, while a parabola is connected; they are not homeomorphic either.
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