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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Hindawi Limited
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/9602504 |
| Summary: | 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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| ISSN: | 2314-8896 2314-8888 |