Let T {R, } U {GkER} be the class of subsets of the plane R where...
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Let T {R, } U {GkER} be the class of subsets of the plane R where Gk = {(x, y) x,y ER, x > y + k} (i) (ii) Prove that T is a topology on R. Is T a topology on R2 if "k ER" is replaced by "kEN"? by "kEQ"? Let T {R, } U {GkER} be the class of subsets of the plane R where Gk = {(x, y) x,y ER, x > y + k} (i) (ii) Prove that T is a topology on R. Is T a topology on R2 if "k ER" is replaced by "kEN"? by "kEQ"?
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