(a) Let S={0,1,1/2,1/3,1/4, . . . ,1/n, . . .}. Prove that S isclosed in the euclidean topology on R.(b) What if we remove the 0 in S? Is the set T={1,1/2,1/3,1/4, .. . ,1/n, . . .}also closed in R? Justify your answer.

匿名用户 最后更新于 2021-12-01 19:16 数学类Mathematics

(a) Let S={0,1,1/2,1/3,1/4, . . . ,1/n, . . .}. Prove that S isclosed in the euclidean topology on R.

(b) What if we remove the 0 in S? Is the set T={1,1/2,1/3,1/4, .. . ,1/n, . . .}also closed in R? Justify your answer.

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