Which of the following statements are true and why?
1.Any continuous function from the open unit interval (0,1) to itself has a fixed point.
2.logx is uniformly continuous on (1/2,+∞) .
3.If A,B are closed subsets of [0,∞) , then A+B={x+y|x∈A,y∈B} is closed in [0,∞)
4.A bounded continuous function on R is uniformly continuous.
5.Suppose f n (x) is a sequence of continuous functions on the closed interval [0,1] converging to 0 pointwise. Then the integral ∫ 1 0 f n (x)dx converges to 0 .
1
Expert's answer
2012-10-04T08:21:03-0400
1.No. Fixed point is f(x)=x. Any words about "open unit intervals"
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