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Question: let be the set of infinite sequences with coordinatewise addition...

Question details

let K^infty be the set of infinite sequences (a1, a2,dg, ), aneA with coordinatewise addition and multiplication.

Determine (prove or give a reason) which of the following subsets of K^infty are subspaces

(a) the set of sequences with only finitely many anメ0

(b) the set of sequences with only finitely many an-0

(c) (K=R)The set of sequences such that limn-tan

(d)(K=R)The set of sequences such that lim_{n o infty } a_n = 1

(e)(K=R)The set of sequences such that sup_n left | a_n ight | < infty

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