Distance to Spaces of Semicontinuous and Continuous Functions. (8th May 2019) - Angosto, Carlos
Abstract : Given a topological spaceX, we establish formulas to compute the distance from a functionf ∈ R X 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.