Dedekind Order Completion ofC(X) by Hausdorff Continuous Functions

DOI10.2989/16073600409486091zbMath1062.54017arXivmath/0407272OpenAlexW1975397112MaRDI QIDQ4661999

Roumen Anguelov

Publication date: 30 March 2005

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407272

zbMATH Keywords

Dedekind completioninterval valued functionHausdorff continuous

Mathematics Subject Classification ID

Set-valued functions (26E25) Function spaces in general topology (54C35) Nonlinear first-order PDEs (35F20) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Real-valued functions in general topology (54C30)

Related Items (21)

Normal semicontinuity and the Dedekind completion of pointfree function rings ⋮ Algebraic and topological structure of some spaces of set-valued maps ⋮ Product ordered Hausdorff continuous \(\mathbb{R}^n\)-interval functions ⋮ Unnamed Item ⋮ Vector-valued interval functions and the Dedekind completion of \(C(X,E)\) ⋮ Hausdorff continuous interval-valued functions and quasicontinuous functions ⋮ Riesz spaces of normal semicontinuous functions ⋮ The universal completion of \(C(X)\) and unbounded order convergence ⋮ On the universal completion of pointfree function spaces ⋮ The order completion method for systems of nonlinear PDEs: solutions of initial value problems ⋮ Convergence of sequences of semi-continuous functions ⋮ Solving large classes of nonlinear systems of PDEs ⋮ The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives ⋮ A lattice-theoretic approach to arbitrary real functions on frames ⋮ The Dedekind Completion of C(X) with Pointwise Discontinuous Functions ⋮ The Riesz Space of Minimal Usco Maps ⋮ Solutions of smooth nonlinear partial differential equations ⋮ The set of Hausdorff continuous functions -- the largest linear space of interval functions ⋮ The convergence space of minimal USCO mappings ⋮ Category measures, the dual of $\mathrm {C}(K)^{\delta }$ and hyper-Stonean spaces ⋮ The order completion method for systems of nonlinear PDEs revisited

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