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Journal of Function Spaces
Volume 2019, Article ID 9602504, 7 pages
https://doi.org/10.1155/2019/9602504
Research Article

Distance to Spaces of Semicontinuous and Continuous Functions

Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain

Correspondence should be addressed to Carlos Angosto; se.tcpu@otsogna.solrac

Received 22 March 2019; Accepted 16 April 2019; Published 8 May 2019

Academic Editor: Miguel Martin

Copyright © 2019 Carlos Angosto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Given a topological space , we establish formulas to compute the distance from a function 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.