Let (S) be a metric space and suppose that p :S x S-R is defined by d(r, y) 1+ d(x, y) pla, y) = for all points xyE S. 2.1.1 Determine whether p satisfies the triangle inequality or not. 2.1.2 Show that (S.2) is bounded and that p(xx) s d(xj) for all x.x E S.

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