- #36

pasmith

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cianfa72 said:Sorry, I believe your equivalence relation ##\sim## first glues theverticaledges together to form a vertically laid down cylinder.

Yes, I meant the vertical sides.

Then, starting from thisintrinsicdefinition of the 2-sphere as quotient, one can define an embedding in ##\mathbb R^3##.

By the obvious [itex](\theta, \phi) = (\pi(1 - y),2\pi x)[/itex].

Btw, in your definition of equivalence relation ##\sim##, why there is the last term ##x_1=x_2 \text { and } y_1=y_2## ?

An equivalence relation is by definition reflexive, so [itex](x,y) \sim (x,y)[/itex] must always hold.