On affinity of Peano type functions

Tomasz Słonka. "On affinity of Peano type functions." Colloquium Mathematicae 127.2 (2012): 233-242. <http://eudml.org/doc/284105>.

@article{TomaszSłonka2012,
abstract = {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 $y ∈ x +(-c,c) × ℝ^\{n-1\}$.},
author = {Tomasz Słonka},
journal = {Colloquium Mathematicae},
keywords = {continuum hypothesis; affinity; Peano function},
language = {eng},
number = {2},
pages = {233-242},
title = {On affinity of Peano type functions},
url = {http://eudml.org/doc/284105},
volume = {127},
year = {2012},
}

TY - JOUR
AU - Tomasz Słonka
TI - On affinity of Peano type functions
JO - Colloquium Mathematicae
PY - 2012
VL - 127
IS - 2
SP - 233
EP - 242
AB - 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 $y ∈ x +(-c,c) × ℝ^{n-1}$.
LA - eng
KW - continuum hypothesis; affinity; Peano function
UR - http://eudml.org/doc/284105
ER -