On Darboux functions \(f\: \mathbb R^n\to \mathbb R^m\) with finite variation (Q2774510)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On Darboux functions \(f\: \mathbb R^n\to \mathbb R^m\) with finite variation |
scientific article; zbMATH DE number 1713820
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Darboux functions \(f\: \mathbb R^n\to \mathbb R^m\) with finite variation |
scientific article; zbMATH DE number 1713820 |
Statements
28 February 2002
0 references
Darboux functions in the sense of Pawlak
0 references
quasi-continuous functions
0 references
cliquish functions
0 references
porosity
0 references
finite variation
0 references
Banach indicatrix
0 references
On Darboux functions \(f\: \mathbb R^n\to \mathbb R^m\) with finite variation (English)
0 references
The main result: In the space of all bounded P-Darboux and cliquish functions from \({\mathbb R}^n\) into \({\mathbb R}^m\) (where \(m\leq 2\)) with finite variation (considered with the metric of uniform convergence) the family of all quasi-continuous functions constitute a porous set. (A function \(f: X\to Y\) is called P-Darboux if \(f(L)\) is connected for any arc \(L\subset X\).) See also \textit{A. Rychlewicz} [Real Anal. Exch. 19, No. 2, 547-563 (1994; Zbl 0810.26006)].
0 references
