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GATE Mathematics 2014 Paper

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Question : 13

Total: 55

Let E1‌and‌E2 be two non empty subsets of a normed linear space X and let E1+E2:= {x+y∈X:x∈E1‌and‌y∈E2} . Then which of the following statements is FALSE

If E1‌and‌E2 are convex, then E1+E2 is convex
If E1‌or‌E2 is open, then E1+E2 is open
E1+E2 must be closed if E1‌and‌E2 are closed
If E1 is closed and E2 is compact, then E1+E2 is closed

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