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Jul21-11, 02:24 PM
micromass's Avatar
P: 18,345
Product of compact sets compact in box topology?

Quote Quote by spicychicken View Post
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
Such a sets will always be empty. Try to consider a cover by all sets of the form

[tex]\prod_{n\in \mathbb{N}}{A_i}[/tex]

Where Ai=[0,0.6[ or Ai=]0.5,1]