A parametrized version of the Borsuk-Ulam theorem
نویسندگان
چکیده
منابع مشابه
A parametrized version of the Borsuk Ulam theorem
The main result of this note is a parametrized version of the BorsukUlam theorem. Loosely speaking, it states that for a map X × S → S (with k < n), considered as a family of maps from S to S, the set of solutions to the Borsuk-Ulam problem (i.e. opposite points in S with the same value) depends continuously on X. We actually formuate this for correspondences. The “continuity” is measured by th...
متن کاملThe Borsuk-Ulam Theorem
I give a proof of the Borsuk-Ulam Theorem which I claim is a simplified version of the proof given in Bredon [1], using chain complexes explicitly rather than homology. Of course this is a matter of taste, and the mathematical content is identical, but in my opinion this proof highlights precisely where and how the contradiction arises. 1 Statements and Preliminaries Theorem 1.1 (Borsuk-Ulam). ...
متن کاملDigital Borsuk-Ulam theorem
The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.
متن کاملThe Borsuk-Ulam Theorem
For simplicity, we adopt the following rules: a, b, x, y, z, X, Y , Z denote sets, n denotes a natural number, i denotes an integer, r, r1, r2, r3, s denote real numbers, c, c1, c2 denote complex numbers, and p denotes a point of En T. Let us observe that every element of IQ is irrational. Next we state a number of propositions: (1) If 0 ≤ r and 0 ≤ s and r2 = s2, then r = s. (2) If frac r ≥ fr...
متن کاملExtensions of the Borsuk-Ulam Theorem
Extensions of the Borsuk-Ulam Theorem by Timothy Prescott
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2011
ISSN: 0024-6093
DOI: 10.1112/blms/bdr037