On affinity of Peano type functions

Tomasz Słonka

Colloquium Mathematicae, Tome 126 (2012), p. 233-242 / Harvested from The Polish Digital Mathematics Library

Résumé

We show that if n is a positive integer and $2^{ℵ₀} ≤ ℵₙ$, then for every positive integer m and for every real constant c > 0 there are functions $f₁,...,f_{n+m}: ℝⁿ → ℝ$ such that $(f₁,...,f_{n+m})(ℝⁿ) = ℝ^{n+m}$ and for every x ∈ ℝⁿ there exists a strictly increasing sequence (i₁,...,iₙ) of numbers from 1,...,n+m and a w ∈ ℤⁿ such that $(f_{i₁},...,f_{iₙ})(y) = y + w$ for $y ∈ x +(-c,c) × ℝ^{n-1}$.

Détail

Publié le : 2012-01-01

Zbl 1255.26005

EUDML-ID : urn:eudml:doc:284105