Convergence of sequences of semi-continuous functions

DOI10.1016/j.jmaa.2011.09.063zbMath1235.26005OpenAlexW2060809327MaRDI QIDQ663624

Jan Harm van der Walt

Publication date: 27 February 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.09.063

zbMATH Keywords

pointwise convergencecontinuous convergenceorder convergencesemi-continuous functions

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (5)

Unnamed Item ⋮ The universal completion of \(C(X)\) and unbounded order convergence ⋮ Differential algebras of generalised functions with dense singularities ⋮ The Riesz Space of Minimal Usco Maps ⋮ Order and uo-convergence in spaces of continuous functions

Cites Work

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• The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives
• The order completion method for systems of nonlinear PDEs revisited
• The set of Hausdorff continuous functions -- the largest linear space of interval functions
• Order convergence structure onC(X)
• When is every Hausdorff continuous interval-valued function bounded by continuous functions?
• The completion of uniform convergence spaces and an application to nonlinear PDEs
• Pointwise and order convergence for spaces of continuous functions and spaces of Baire functions
• Dedekind Order Completion ofC(X) by Hausdorff Continuous Functions
• The Uniform Order Convergence Structure onML(X)
• The Normal Completion of the Lattice of Continuous Functions

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