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Let be the equivalence relation x1 x2 y1 y2 iff x2 y2

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Reference no: EM13582518

Examples of quotient spaces

1. Let ~ be the equivalence relation (x1, x2) ~ (y1, y2) iff x2 = y2 on R2. Then R2/~ is homeomorphic to R.

2. Let ~ be the equivalence relation x ~ y iff x and y are diametrically opposite, on S1. Then S1/~ is homeomorphic to S1. Is the corresponding result for S2 true?

Note: Sn : the n-sphere, {x ?Rn+1 | |x| =1}

S1 is the unit circle inR2.

Reference no: EM13582518

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