Given a metric space R³, where the metric o is defined by o(x, y) = { 1 if x+y if z=y z,y ER¹ (a) Describe the open sets and closed sets in the given metric space. Give specific examples, and provide reasons for them being open and/or closed. (b) Find a sequence (Zn)neN that converges to a limit a € R³. Show that your sequence does indeed converge. (e) Would you say that the given metric space is complete? Justify your answer. (d) Find the cluster points of this metric space, if any. Show your working.

Q: (-14) + (–7)

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