Brouwer Fixed Point Theorem for Simplexes
نویسندگان
چکیده
منابع مشابه
Brouwer Fixed Point Theorem for Simplexes
In this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of E. First we introduce the Lebesgue number, which for an arbitrary open cover of a compact metric space M is a positive real number so that any ball of about such radius must be completely contained in a member of the cover. Then we introduce the...
متن کاملThe Brouwer Fixed Point Theorem for Intervals1
(1) If a≤ c and d ≤ b, then [c,d]⊆ [a,b]. (2) If a≤ c and b≤ d and c≤ b, then [a,b]∪ [c,d] = [a,d]. (3) If a≤ c and b≤ d and c≤ b, then [a,b]∩ [c,d] = [c,b]. (4) For every subset A of R1 such that A = [a,b] holds A is closed. (5) If a≤ b, then [a, b]T is a closed subspace of R1. (6) If a≤ c and d ≤ b and c≤ d, then [c, d]T is a closed subspace of [a, b]T. (7) If a≤ c and b≤ d and c≤ b, then [a,...
متن کاملSpherical Designs via Brouwer Fixed Point Theorem
For each N ≥ cdn 2d(d+1) d+2 we prove the existence of a spherical ndesign on Sd consisting of N points, where cd is a constant depending only on d.
متن کاملA Brouwer fixed point theorem for graph endomorphisms
We prove a Lefschetz formula L(T ) = ∑ x∈F iT (x) for graph endomorphisms T : G→ G, where G is a general finite simple graph and F is the set of simplices fixed by T . The degree iT (x) of T at the simplex x is defined as (−1)dim(x)sign(T |x), a graded sign of the permutation of T restricted to the simplex. The Lefschetz number L(T ) is defined similarly as in the continuum as L(T ) = ∑ k(−1)tr...
متن کاملComputable counter-examples to the Brouwer fixed-point theorem
This paper is an overview of results that show the Brouwer fixed-point theorem (BFPT) to be essentially non-constructive and noncomputable. The main results, the counter-examples of Orevkov and Baigger, imply that there is no procedure for finding the fixed point in general by giving an example of a computable function which does not fix any computable point. Research in reverse mathematics has...
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: Formalized Mathematics
سال: 2011
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-011-0023-4