Metric spaces of semicontinuous functions
type: Item
instance of: scholarly article
title: Metric spaces of semicontinuous functions
zbMATH Open document ID: 0906.54013
DOI: 10.1007/BF02110780
author: E. P. Dolzhenko
author: E. A. Sevast'yanov
published in: Mathematical Notes
publication date: 1995-07-10T00:00:00Z
review text: A metric in the spaces of bounded upper-semicontinuous real functions defined on the \(n\)-dimensional interval is introduced -- useful in some applications -- with which the spaces \(MS(I)\) and \(DS(I)\) are separable. Here \(MS(I)\) denotes the set of all real bounded upper-semicontinuous functions on the interval \(I\) and \(DS(I)\) denotes the set of all nonnegative bounded upper-semicontinuous functions on the interval \(I.\) Moreover, the space \(DS(I)\) is complete while \(MS(I)\) is not complete.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 771988
zbMATH Keywords: semicontinuous functions
zbMATH Keywords: metric spaces of functions
reviewed by: Jacek Jędrzejewski
MaRDI profile type: Publication
cites work: Q4839164
Recommended article: Q4368243
Recommended article: Metrically separable and approximately continuous functions
Recommended article: Q4720378
Recommended article: Distance to spaces of semicontinuous and continuous functions
Recommended article: Q3411867
Recommended article: Metric spaces on which continuous functions are ``almost'' uniformly continuous
Recommended article: Q3095857
Recommended article: Q3133737
Recommended article: Metrizability of the space of quasicontinuous functions
description: scientific article; zbMATH DE number 771988