it is easy to construct a map from S^2 to S^2, with covering time being unity(adsbygoogle = window.adsbygoogle || []).push({});

but how to do the similar task on the projected manifold RP^2=S^2/Z_2?

i tried to use the stereographical trick

the points on the lower half semisphere are projected onto the plane

the problem is that the infinity point on the plane is mapped to the circle, which is not a single point on RP^2.

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# How to construct a map from S^2 to RP^2 with covering time being unity?

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