In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points...

above, although "Ulam did make a fundamental contribution in proposing" the Borsuk–Ulam theorem. The two-dimensional variant of the theorem (also known as...

invariance of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology. The theorem is also used for proving deep...

Using the Borsuk–Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry is a graduate-level mathematics textbook in topological combinatorics...

simplex, gives the Borsuk–Ulam theorem, that ƒ must map two opposite points of the sphere to the same point. The topological Radon theorem was originally...

{\displaystyle \vert f(x)\vert <\varepsilon } . A similar result is the Borsuk–Ulam theorem, which says that a continuous map from the n {\displaystyle n} -sphere...

proved a number of theorems and proposed several conjectures. Born into a wealthy Polish Jewish family in Lemberg, Austria-Hungary; Ulam studied mathematics...

Warszawa. Zygmunt Janiszewski Stanislaw Ulam Scottish Café Animal Husbandry, an educational dice game published by Borsuk at his own expense in 1943 during...

In mathematics, the Lusternik–Schnirelmann theorem, aka Lusternik–Schnirelmann–Borsuk theorem or LSB theorem, says as follows. If the sphere Sn is covered...

Blakers–Massey theorem Borsuk–Ulam theorem Brouwer fixed point theorem Cellular approximation theorem Dold–Thom theorem Eilenberg–Ganea theorem Eilenberg–Zilber...

1515/9781400877492. ISBN 978-1-4008-7749-2. Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...

158–164, doi:10.1112/jlms/s2-23.1.158 Matoušek, Jiří (2007), Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...

In mathematics, Tucker's lemma is a combinatorial analog of the Borsuk–Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed...

any symmetry possessed by both spaces. A famous theorem of equivariant topology is the Borsuk–Ulam theorem, which asserts that every Z 2 {\displaystyle \mathbf...

language Borsuk–Ulam theorem Erdős–Ulam problem Fermi–Pasta–Ulam–Tsingou problem Hyers–Ulam–Rassias stability Kuratowski–Ulam theorem Mazur–Ulam theorem Ulam's...

complex Tucker's lemma Simplex tree Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...

numbers n. The case when n = 2 can be considered an application of the Borsuk–Ulam theorem to the real line. It says that if f ( x ) {\displaystyle f(x)} is...

ISBN 0-521-79160-X and ISBN 0-521-79540-0 Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...

geometry) Borsuk–Ulam theorem (topology) Bott periodicity theorem (homotopy theory) Bounded convergence theorem (measure theory) Bounded inverse theorem (operator...

F.W. Simmons and F.E. Su (2003). "Consensus-halving via theorems of Borsuk-Ulam and Tucker" (PDF). Mathematical Social Sciences. 45: 15–25. doi:10...

subsets are not enough in general. The proof is based on the Borsuk–Ulam theorem. That led Borsuk to a general question: Die folgende Frage bleibt offen: Lässt...

combinatorics. Lovász's proof used the Borsuk–Ulam theorem and this theorem retains a prominent role in this new field. This theorem has many equivalent versions...

p. 58. ISBN 978-0-48627576-5. Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...

proved by the Borsuk-Ulam theorem. When k {\displaystyle k} is an odd prime number, the proof involves a generalization of the Borsuk-Ulam theorem. When k {\displaystyle...

emanating from the centre, and these two points are antipodal. The Borsuk–Ulam theorem is a result from algebraic topology dealing with such pairs of points...

combinatorics. Lovász's proof used the Borsuk-Ulam theorem and this theorem retains a prominent role in this new field. This theorem has many equivalent versions...

theorem Brouwer fixed point theorem Invariance of domain Lefschetz fixed-point theorem Hairy ball theorem Degree of a continuous mapping Borsuk–Ulam theorem...

This is a direct corollary of the Hobby–Rice theorem. It can also be proved using the Borsuk-Ulam theorem: Every partition of an interval using n {\displaystyle...

fact can be used to give proofs of the Brouwer fixed point theorem and the Borsuk–Ulam theorem in dimension 2. The fundamental group of the figure eight...

any k ≥ 1 {\displaystyle k\geq 1} ) vanishes at some point. The Borsuk–Ulam theorem: any continuous function from an n-sphere into Euclidean n-space...