Variations on products and quotients of Darboux functions
type: Item
instance of: scholarly article
title: Variations on products and quotients of Darboux functions
zbMATH Open document ID: 0711.26004
author: Tomasz Natkaniec
author: Waldemar Orwat
published in: Real Analysis Exchange
publication date: 1990-01-01T00:00:00Z
review text: A. M. Bruckner and the reviewer proved that if a Darboux function f: \(R\to R\) is constant on no subinterval and D is a countable dense subset of R, then there exists a function g taking on all values in each interval such that the range of \(f+g\) is D. This paper contains a number of variants of this result replacing sums by products and quotients, considering the domain of f to be various subsets of R and letting g take on each value c-times in each interval. In particular, there is a characterization of those functions which can be a quotient of Darboux functions. (This corrects an assertion of the reviewer.)
Mathematics Subject Classification ID: 26A15
zbMATH DE Number: 4168971
zbMATH Keywords: products
zbMATH Keywords: quotients
zbMATH Keywords: Darboux functions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4168971