Is the space of bounded, convex, continuous functions with the sup norm complete?
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3Surely yes. have you made an attempt? Tell us where you are stuck. – Kavi Rama Murthy Sep 27 '18 at 05:25
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I am stuck on the convex part. I essentially followed the ideas from https://math.stackexchange.com/questions/71121/space-of-bounded-continuous-functions-is-complete?rq=1 – eulerup Sep 27 '18 at 05:30
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2Even pointwise limit of convex functions is convex. Apply the definition and take limits on both sides. – Kavi Rama Murthy Sep 27 '18 at 05:32