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3. Let X be the set of positive integers. For each n E X, let Sn = {k € X: k2n}. Show that T = {S: ne X} U {0} is a topology for X, and find. the closure of the set of even integers. Find the closure of the singleton set. A = {100}.

3. Let X be the set of positive integers. For each n E X, let Sn = {k € X: k2n}. Show that T = {S: ne X} U {0} is a topology for X, and find. the closure of the set of even integers. Find the closure of the singleton set. A = {100}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Let X be the set of positive integers. For each n E X, let Sn = {k € X: k≥n}. Show that T = {Sn: ne X} U {0} is a topology for X, and find the closure of the set of even integers. Find the closure of the singleton set. A = {100}.
Transcribed Image Text:3. Let X be the set of positive integers. For each n E X, let Sn = {k € X: k≥n}. Show that T = {Sn: ne X} U {0} is a topology for X, and find the closure of the set of even integers. Find the closure of the singleton set. A = {100}.
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