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**1. The question is to show whether A is compact in R2 with the standard topology. A = [0,1]x{0} U {1/n, n[tex]\in[/tex] Z+} x [0,1]**

**3. If I group the [0,1] together, I get [0,1] x {0,1/n, n [tex]\in[/tex] Z+ }, and [0,1] is compact in R because of Heine Borel and {0}U{1/n} is compact since you can show that every cover has a finite subcover. Now, if you take the product of two compact sets will they still be compact? Tychonoff's theorem says product of compact spaces is compact, but I'm not too sure if it applies here.**

Thanks in advance.

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