Solved: Examples of quotient spaces, Business Management

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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.

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Solution Preview :

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Business Management: Examples of quotient spaces

Reference No:- TGS0687360

Have a Question? (oR Write a Review)

Recent Questions Asked Business Management

Q : Contract requirements at a minimum total interviewing cost

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Solution Preview :

Prepared by a verified Expert

Business Management: Examples of quotient spaces

Reference No:- TGS0687360

Recent Questions Asked Business Management

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