Equivalence Relation

SOLVED: (a) Define an equivalence relation on the plane X = R2 as follows: Xo X Yo   X1 Xy1 if xo Y = x1 y. Let X* be the corresponding quotient space. It is homeomorphic to a familiar space; what is it? [Hint: Set g(x Xy) =x y2 .] (b) Repeat (a) for the equivalence relation Xo X Yo   X1 Xy1 if x8 y = x y

(a) Define an equivalence relation on the plane X=\mathbb{R}^2 ... | Filo