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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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/9602504 |
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| _version_ | 1832552184523259904 |
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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. |
| format | Article |
| id | doaj-art-c78b9c92e1e643b8b05143f896745770 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |