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
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Source Borsuk-Ulam Theorem (Wikipedia)
Sources
1. Borsuk-Ulam Theorem (Wikipedia)
Wikimedia FoundationHistory section
The first proof was given by Karol Borsuk (1933), where the formulation of the problem was attributed to Stanisław Ulam.
In Group: Algebraic Topology, Lead
In topology, the Borsuk-Ulam theorem states that every continuous map from the sphere to the plane maps some pair of antipodal points to the same point.
View the Source Borsuk-Ulam Theorem (Wikipedia)
Proved By: Karol Borsuk, LeadQuote, Proved By: Karol Borsuk, Lead
The first proof was given by Karol Borsuk (1933), where the formulation of the problem was attributed to Stanisław Ulam.
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