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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.

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.

Advanced Engineering Mathematics
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 = 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 po n-many = (1, 1, 1, ...) € X to be the constant sequence. Prove that {Pn}n>1U {Po} is closed inside of X.
Transcribed Image Text: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 po n-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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