On Whitney pairs

Csörnyei, Marianna

On Whitney pairs

Fundamenta Mathematicae, Tome 159 (1999), p. 63-79 / Harvested from The Polish Digital Mathematics Library

Résumé

A simple arc ϕ is said to be a Whitney arc if there exists a non-constant function f such that $l i m_{x \mapsto x_{0}} (| f (x) - f (x_{0}) |) / (| ϕ (x) - ϕ (x_{0}) |) = 0$ for every $x_{0}$ . G. Petruska raised the question whether there exists a simple arc ϕ for which every subarc is a Whitney arc, but for which there is no parametrization satisfying $l i m_{t \mapsto t_{0}} (| t - t_{0} |) / (| ϕ (t) - ϕ (t_{0}) |) = 0$ . We answer this question partially, and study the structural properties of possible monotone, strictly monotone and VBG* functions f and associated Whitney arcs.

Publié le : 1999-01-01

Zbl 0936.26005

EUDML-ID : urn:eudml:doc:212381

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     author = {Marianna Cs\"ornyei},
     title = {On Whitney pairs},
     journal = {Fundamenta Mathematicae},
     volume = {159},
     year = {1999},
     pages = {63-79},
     zbl = {0936.26005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv160i1p63bwm}
}

Csörnyei, Marianna. On Whitney pairs. Fundamenta Mathematicae, Tome 159 (1999) pp. 63-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv160i1p63bwm/

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