Question: This is topology. 3. [solo] (a) Consider the equivalence relation on R defined by (x1, y1) ~ (x2, y2) if and only if x1 +

This is topology.

3. [solo] (a) Consider the equivalence relation on R defined by (x1, y1) ~ (x2, y2) if and only if x1 + y1 = x2 + y2. Describe the set of points in each equivalence class. What is the quotient space, again up to homeomorphism, that results from considering the set of equivalence classes? (b) Same problem except the equivalence relation is now (x1, y1) ~(x2, y2) if and only if x- + y. = x5+ y

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