Riesz spaces of real continuous functions

Riesz spaces of real continuous functions

An Archimedean Riesz space E is isomorphic to C ( X ) for some completely regular Hausdorff space X if and only if there exists a weak order unit e  > 0 for which E is e -uniformly complete, e -semisimple, e -separating and 2-universally e -complete.

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2010-09, Vol.14 (3), p.473-480
Hauptverfasser: Montalvo, F., Pulgarín, A., Requejo, B.
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Lattice theory
Mathematical functions
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Studies
Topology
Vector space
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Zusammenfassung:An Archimedean Riesz space E is isomorphic to C ( X ) for some completely regular Hausdorff space X if and only if there exists a weak order unit e  > 0 for which E is e -uniformly complete, e -semisimple, e -separating and 2-universally e -complete.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-009-0031-6