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...

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

notable mathematical concepts that bear Borsuk's name include Borsuk's conjecture, Borsuk–Ulam theorem and Bing–Borsuk conjecture. In 1936, he married Zofia...

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...

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...

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

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

{\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 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...

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

1112/jlms/s1-41.1.123 Blagojević, P. V. M.; Ziegler, G. M. (2017), "Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story", in Loebl, M.; Nešetřil, J.; Thomas...

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...

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

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

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...

Bolzano–Weierstrass theorem (real analysis, calculus) Borsuk–Ulam theorem (topology) Brouwer fixed-point theorem (topology) Cantor's intersection theorem (real analysis)...

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

ISBN / Date incompatibility (help) Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...

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...

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...

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...

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...

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...

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...

Mathematical Encyclopaedia (ed. I.M. Vinogradov), a related 1929 theorem (of Knaster, Borsuk and Mazurkiewicz) had also become known as the Sperner lemma...

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...

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

Press. ISBN 978-0-201-62728-2. 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...

Springer-Verlag. p. 9. ISBN 3-540-18190-3. Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry (2nd ed...