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The question is to show that a circle and a elipse are homomorphic in $R^{2}$.

I have two questions 1) should I consider only the boundary points of circles and elipse?

2) what is the suitable function for this?.

Sinchan Bhattacharjee
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    Since you tagged "metric-spaces" did you mean "homeomorphic" instead? And by $R^2$ did you mean the real plane $\mathbb{R}^2$? – saru May 28 '20 at 16:16

1 Answers1

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  1. Usually, yes, we mean only the contour by a 'circle' or 'ellipse'. For the solid circle, we rather use 'disk'. But here it doesn't matter.

  2. In a suitable coordinate system, it's $(x,y)\mapsto (ax, by)$ for some $a,b>0$.

Berci
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