The Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Equivalent statements · Proofs · Equivalent results |
| Теорема Борсука — Улама |  |
Теорема Бо́рсука — У́лама — классическая теорема алгебраической топологии, утверждающая, что всякая непрерывная функция, отображающая -мерную сферу в -мерное евклидово пространство для некоторой пары диаметрально противоположных точек имеет общее... Википедия
Borsuk-Ulam theorem states: Theorem 1. Every continuous mapping of n-dimensional sphere Sn into n- dimensional Euclidean space Rn identifies a pair of antipodes ... |
Then there are two antipodal points on the earth with the same temperature and pressure. The following celebrated theorem is implied by the Borsuk-Ulam Theorem. |
The Borsuk–Ulam theorem from algebraic topology states that for every con- tinuous function from the n-dimensional unit sphere to the (n + 1)-dimensional. |
25 сент. 2017 г. · The Borsuk-Ulam theorem with various generalizations and many proofs is one of the most useful theorems in algebraic topology. |
More formally, it says that any continuous function from an n-sphere to Rn must send a pair of antipodal points to the same point. (So, in the above statement, ... |
Videolar The Borsuk-Ulam theorem is a well-known theorem in algebraic topology which states that if φ : S^n → R^k is a continuous map from the unit n-sphere into the ... |
A Borsuk-Ulam theorem for the finite group G consists of finding a function b: N → N with b(n)→ ∞ as n→ ∞ and such that the existence of a G-map SV→SW ... |
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