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Compact set

Amer

Active member
Mar 1, 2012
275
It is a question from Yahoo, can you look at my answer
The question is
is the set [tex] \{\frac{1}{2} , \frac{2}{3} , \frac{3}{4} , ... \} \cup [ 1, 25] [/tex] compact ?
I took an arbitrary open cover and I proved it has a finite subcover, I used the information that closed and bounded is compact.
Here

 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,701
It is a question from Yahoo, can you look at my answer
The question is
is the set $ \bigl\{\frac{1}{2} , \frac{2}{3} , \frac{3}{4} , \ldots \bigr\} \cup [ 1, 25] $ compact ?
I took an arbitrary open cover and I proved it has a finite subcover, I used the information that closed and bounded is compact.
Here

Your proof in Yahoo Answers is correct. That set is compact. (But you did not use the fact that closed and bounded is compact. Instead, you used the fact that every open cover has a finite subcover, to deduce compactness.)
 

Amer

Active member
Mar 1, 2012
275
Thanks very