Distance to Spaces of Semicontinuous and Continuous Functions

Given a topological space X, we establish formulas to compute the distance from a function f∈RX to the spaces of upper semicontinuous functions and lower semicontinuous functions. For this, we introduce an index of upper semioscillation and lower semioscillation. We also establish new formulas about...

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Main Author: Carlos Angosto
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2019/9602504
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author Carlos Angosto
author_facet Carlos Angosto
author_sort Carlos Angosto
collection DOAJ
description Given a topological space X, we establish formulas to compute the distance from a function f∈RX to the spaces of upper semicontinuous functions and lower semicontinuous functions. For this, we introduce an index of upper semioscillation and lower semioscillation. We also establish new formulas about distances to some subspaces of continuous functions that generalize some classical results.
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institution Kabale University
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publishDate 2019-01-01
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series Journal of Function Spaces
spelling doaj-art-c78b9c92e1e643b8b05143f8967457702025-02-03T05:59:23ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/96025049602504Distance to Spaces of Semicontinuous and Continuous FunctionsCarlos Angosto0Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, SpainGiven a topological space X, we establish formulas to compute the distance from a function f∈RX to the spaces of upper semicontinuous functions and lower semicontinuous functions. For this, we introduce an index of upper semioscillation and lower semioscillation. We also establish new formulas about distances to some subspaces of continuous functions that generalize some classical results.http://dx.doi.org/10.1155/2019/9602504
spellingShingle Carlos Angosto
Distance to Spaces of Semicontinuous and Continuous Functions
Journal of Function Spaces
title Distance to Spaces of Semicontinuous and Continuous Functions
title_full Distance to Spaces of Semicontinuous and Continuous Functions
title_fullStr Distance to Spaces of Semicontinuous and Continuous Functions
title_full_unstemmed Distance to Spaces of Semicontinuous and Continuous Functions
title_short Distance to Spaces of Semicontinuous and Continuous Functions
title_sort distance to spaces of semicontinuous and continuous functions
url http://dx.doi.org/10.1155/2019/9602504
work_keys_str_mv AT carlosangosto distancetospacesofsemicontinuousandcontinuousfunctions