Let X = 1 {0, 1} with the product topology, where each space {0, 1} has the discrete topology.For any choice of n ≥ 1, let pn be the element(1, 1,..., 1, 0, 0, ...) € X.and take pon-many= (1, 1, 1, ...) € X to be the constant sequence. Prove that{Pn}n>1U {Po}is closed inside of X.

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Answered: Let X = {0, 1} with the product…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let X = {0, 1} with the product topology, where each space {0, 1} has the discrete topology. For any choice of n ≥ 1, let pn be the element (1, 1,..., 1, 0, 0, ...) E X. n-many and take p = (1, 1, 1,...) E X to be the constant sequence. Prove that {Pn}n>1U {Po} is closed inside of X.