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Product of compact sets compact in box topology? 
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#1
Jul2011, 11:33 AM

P: 3

So Tychonoff theorem states products of compact sets are compact in the product topology.
is this true for the box topology? counterexample? 


#2
Jul2111, 08:08 AM

Mentor
P: 18,063

A counterexample is [itex]\prod_{n\in \mathbb{N}}{[0,1]}[/itex]. Can you show why?



#3
Jul2111, 01:17 PM

P: 3

if S_n is the set with empty sets in each index except n where for index n you have [0,1], then {S_n} is an open cover with no finite subcover...i think



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