Borsuk's conjecture

Unsolved problem in mathematics

What is the lowest

n

such that not every bounded subset

E

of the space

\mathbb {R} ^{n}

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^{[note 1]} incorrectly called Borsuk's conjecture, is a question in discrete geometry. It is named after Karol Borsuk.

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[note 1]