Any continuous function from an n-dimensional sphere to n-dimensional Euclidean space must map some pair of antipodal points to the same point. Named for Karol Borsuk and Stanislaw Ulam, it has striking consequences, including that at any moment there exist two antipodal points on Earth with equal temperature and equal barometric pressure.
Facts
StatementEvery continuous function from an n-sphere into n-dimensional Euclidean space maps some pair of antipodal points to the same point. 1 Proof YearLyusternik and Shnirelman had already stated the result in 1930; the first full proof, by Karol Borsuk, dates to 1933. Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Borsuk-Ulam Theorem (Wikipedia)
Wikimedia FoundationHistory sectionQuote, History section
The first proof was given by Karol Borsuk (1933), where the formulation of the problem was attributed to Stanisław Ulam.
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