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## Main Question or Discussion Point

So Tychonoff theorem states products of compact sets are compact in the product topology.

is this true for the box topology? counterexample?

is this true for the box topology? counterexample?

- Thread starter spicychicken
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So Tychonoff theorem states products of compact sets are compact in the product topology.

is this true for the box topology? counterexample?

is this true for the box topology? counterexample?

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

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- #4

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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 A

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