Question: Let S be the unit two sphere in R centered at the origin. Consider an equivalence relation on X = S x [0, 1]

Let S be the unit two sphere in R centered at the

Let S be the unit two sphere in R centered at the origin. Consider an equivalence relation on X = S x [0, 1] defined by (x, i)~ (y,j) x = y, i=0, and j = 1. Show that X/ ~ is a compact and connected 3-manifold that is imbed- dable in R5.

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