2. For any n E N, let G, denote the interval (-). Prove that each G, is an open set in R and each G, is not a closed set in R. Let G =N Gm. Lastly, explain why G is not an open set. (You are showing that an infinite intersection of open sets is not necessarily open.) Hint: For latter question, find all the elements in G.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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2. For any n e N, let G, denote the interval (- ). Prove that each G, is an open set
in R and each G, is not a closed set in R. Let
G = N G..
n=1
Lastly, explain why G is not an open set. (You are showing that an infinite intersection
of open sets is not necessarily open.)
Hint: For latter question, find all the elements in G.
Transcribed Image Text:2. For any n e N, let G, denote the interval (- ). Prove that each G, is an open set in R and each G, is not a closed set in R. Let G = N G.. n=1 Lastly, explain why G is not an open set. (You are showing that an infinite intersection of open sets is not necessarily open.) Hint: For latter question, find all the elements in G.
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