For each description below, provide a specific example fitting thedescription (p

Question

For each description below, provide a specific example fitting thedescription (provide some justification), or else explain why nosuch example exists.

1)An open set with no accumulation point

2)A subset of [0,sqrt{2}] of Lebesgue measure 1 which contains nointerval

3)A subset of [0,sqrt{2}] of Lebesgue measure 1 with noaccumulation point

4)A bounded set with Lebesgue measure infinity

5)An open set with Lebesgue measure 0

6)A function that has all its derivative at p = 3 but is notanalytic there

7)A sequence of functions on $R$, all continuous everywhere, allnon differentiable at 0, that converge uniformly to a functiondifferentiable everywhere

8)A series of functions which converges to (sin[3x])/x

Explanation / Answer

(1) the null set is an open set in which there are noaccumulation points.

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