Various continuities with the density, \(\mathcal I\)-density and ordinary topologies on \(\mathbb{R}\)
type: Item
instance of: scholarly article
title: Various continuities with the density, \(\mathcal I\)-density and ordinary topologies on \(\mathbb{R}\)
zbMATH Open document ID: 0757.26005
published in: Real Analysis Exchange
publication date: 1992-09-26T00:00:00Z
review text: The aim of the paper is to investigate sixteen classes of continuous real functions of a real variable which are obtained when the domain and the range are equipped with one of the following topologies: the ordinary topology, density topology, \(I\)-density topology and deep \(I\)-density topology. It turns out that some of these classes consist only of constant functions. The inclusions between more interesting classes are presented in several diagrams. Also the relationship between them and analytic, \(C^ \infty\), Baire*1 and Baire 1 functions is studied. The proofs are developed with the techniques prepared in earlier papers by the same authors.
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 26E10
zbMATH DE Number: 54503
zbMATH Keywords: analytic functions
zbMATH Keywords: \(C^ \infty\)-functions
zbMATH Keywords: Baire*1 functions
zbMATH Keywords: \(I\)- density topology
zbMATH Keywords: deep \(I\)-density topology
zbMATH Keywords: continuous real functions
zbMATH Keywords: range
zbMATH Keywords: ordinary topology
zbMATH Keywords: density topology
zbMATH Keywords: Baire 1 functions
author: Krzysztof Chris Ciesielski
author: Lee Larson
reviewed by: Jerzy Niewiarowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 54503