Question: Let X be the closed unit interval [0. 1]. Consider the Euclidean metric space ([0. 1], d) with distance function d (x; y) = |x

Let X be the closed unit interval [0. 1]. Consider the Euclidean metric space ([0. 1], d) with distance function d (x; y) = |x - y| for all x. y E X. Specify for the following subsets of X whether they are convex as well as closed or/and open in this Euclidean topology: (i) [0, 1- - for some n E N (1i) UnEN [0, 1 - = ] (iii) (0. = ) for some ne

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