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...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2011
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-011-0023-4