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Let X be the space of all continuous functions from [0, 1] to [0, 1] equipped...

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Advance Math

Let X be the space of all continuous functions from [0, 1] to[0, 1] equipped with the sup metric. Let Xi be the set of injectiveand Xs be the set of surjective elements of A and let Xis = Xi ∩Xs. Prove or disprove: i) Xi is closed, ii) Xs is closed, iii) Xisis closed, iv) X is connected, v) X is compact.

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