On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space

Artur Michalak. "On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space." Bulletin of the Polish Academy of Sciences. Mathematics 62.1 (2014): 61-76. <http://eudml.org/doc/281335>.

@article{ArturMichalak2014,
abstract = {We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function $f:[0,1]^m → X$ is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function $f:[0,1]^m → X$ with respect to any norming subset there exists a separately increasing function $g:[0,1]^m → ℝ$ such that the sets of points of discontinuity of f and g coincide.},
author = {Artur Michalak},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {increasing vector functions},
language = {eng},
number = {1},
pages = {61-76},
title = {On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space},
url = {http://eudml.org/doc/281335},
volume = {62},
year = {2014},
}

TY - JOUR
AU - Artur Michalak
TI - On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2014
VL - 62
IS - 1
SP - 61
EP - 76
AB - We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function $f:[0,1]^m → X$ is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function $f:[0,1]^m → X$ with respect to any norming subset there exists a separately increasing function $g:[0,1]^m → ℝ$ such that the sets of points of discontinuity of f and g coincide.
LA - eng
KW - increasing vector functions
UR - http://eudml.org/doc/281335
ER -