mathematics, 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...

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

pancakes simultaneously. The ham sandwich theorem can be proved as follows using the Borsuk–Ulam theorem. This proof follows the one described by Steinhaus...

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...

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...

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...

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

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...

conjecture, thus beginning the new field of topological combinatorics. Lovász's proof used the Borsuk–Ulam theorem and this theorem retains a prominent role...

the infinite-dimensional topology. Some of the notable mathematical concepts that bear Borsuk's name include Borsuk's conjecture, Borsuk–Ulam theorem...

x} in the unit interval such that | f ( x ) | < ε {\displaystyle \vert f(x)\vert <\varepsilon } . A similar result is the Borsuk–Ulam theorem, which...

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

be continuously shrunk to a single point. This can be proved using the Borsuk–Ulam theorem. Proving that conn π ( S d ) ≥ d − 1 {\displaystyle {\text{conn}}_{\pi...

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

Reviews, Bulletin of the London Mathematical Society, 35 (5): 719–720, doi:10.1112/S0024609303269332. Review of Using the Borsuk-Ulam theorem by Zdzisław Dzedzej...

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

Kathryn L.; Su, Francis Edward (2013), "A Borsuk–Ulam equivalent that directly implies Sperner's lemma", The American Mathematical Monthly, 120 (4): 346–354...

Mapping cone (topology) Join (topology) Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry...

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...

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

lemma is a combinatorial analog of the Borsuk–Ulam theorem, named after Albert W. Tucker. Let T be a triangulation of the closed n-dimensional ball B n {\displaystyle...

algorithms. According to the Soviet Mathematical Encyclopaedia (ed. I.M. Vinogradov), a related 1929 theorem (of Knaster, Borsuk and Mazurkiewicz) had also...

giving rise to the field of topological combinatorics. Soon thereafter Imre Bárány gave a simple proof, using the Borsuk–Ulam theorem and a lemma of David...

conjecture, thus beginning the new study of topological combinatorics. Lovász's proof used the Borsuk-Ulam theorem and this theorem retains a prominent role...

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...

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...

ISBN 978-0-444-82432-5, retrieved 2022-11-15 Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry...

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

Westview Press. ISBN 978-0-201-62728-2. Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry...

ISBN 978-0-444-82432-5, retrieved 2022-11-15 Matoušek, Jiří (2007). Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry...