Let [tex] B_n=\cup_{i=1}^n A_i [/tex].(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \overline{B_n}[/tex] is the smallest closed subset containing [tex] B_n[/tex].

Note that

[tex]\cup_{i=1}^n \overline{A_i}[/tex] is a closed subset containing [tex] B_n[/tex].

Thus,

[tex] \overline{B_n}\supset \cup_{i=1}^n \overline{A_i}[/tex]

Isn't the truth should be that

[tex] \overline{B_n}[/tex] is the smallest?

How come claim that

[tex]\cup_{i=1}^n \overline{A_i}[/tex] is even smaller?

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# A mistake from Rudin analysis?

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