On continuous and quasi-continuous functions
type: Item
instance of: scholarly article
title: On continuous and quasi-continuous functions
zbMATH Open document ID: 0810.26006
author: Andrzej Rychlewicz
published in: Real Analysis Exchange
publication date: 1995-04-02T00:00:00Z
review text: In this paper, there is an answer to the question if continuous functions constitute a porous set in the space of bounded Darboux functions \(f: \mathbb{R}^ 2\to \mathbb{R}^ 2\) with finite variation, equipped with the metric of uniform convergence. The answer is yes! But it was proved more: The space of continuous functions is the porous set in the same space which is a subset of the space of Darboux functions with finite variation.
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A21
zbMATH DE Number: 627519
zbMATH Keywords: quasi-continuous functions
zbMATH Keywords: continuous functions
zbMATH Keywords: porous set
zbMATH Keywords: space of bounded Darboux functions
reviewed by: Ryszard Pawlak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 627519