Borsuk's conjecture

Unsolved problem in mathematics
What is the lowest n such that not every bounded subset E of the space can be partitioned into (n + 1) sets, each of which has a smaller diameter than E?
More unsolved problems in mathematics

The Borsuk problem in geometry, for historical reasons incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk.

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