# Compactness is not box product-closed

From Topospaces

This article gives the statement, and possibly proof, of a topological space property (i.e., compact space)notsatisfying a topological space metaproperty (i.e., box product-closed property of topological spaces).

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## Statement

It is possible to have a collection of topological spaces, each of which is a compact space, but such that the product , is not a compact space under the box topology.

## Related facts

- Compactness is product-closed under the product topology. For finite products, this can be even more easily proved using the tube lemma