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Are these two open balls the same as each other

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Question 2.

(1) * In this question we will think about the metrics d1 and dsup defined in lectures on C[0, 1] the set of continuous functions on the closed interval [0, 1]. Let ζ ∈ C[0, 1] be the zero function, i.e., the function given by ζ(t) = 0 for all t ∈ [0, 1]. Describe what elements of C[0, 1] lie in the open ball B1(ζ) for each of the metrics d1 and dsup. Are these two open balls the same as each other? Is one a subset of the other?

(2) What would your answers be if we considered the open balls B(ζ) for different values of ? What if we also thought about the balls for the the d2 metric?

Reference no: EM131028843

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