Z-mappings and a classification theorem

Shi, Guang; Wang, G. P.

doi:10.1007/bf02574110

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A Primer On Z-theory For Continuous Posets and Domains1

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2010

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“…The suggestion of [72] to apply subset systems to the theory of continuous posets was followed by Nelson [51], Novak [55], Bandelt [6], Bandelt and Erné [7], [8], and this research was carried on by Venugopalan [70], [71], Xu [73], Baranga [9], Menon [49], Shi and Wang [65], Erné [20], [23] among others. Conditions iq and iiq together ensure that each ZrP s contains all singletons.…”

Section: A Primer On Z-theory For Continuous Posets and Domainsmentioning

confidence: 99%

What is the role of continuity in continuous linear forms representation?

Poncet

2010

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The recent extensions of domain theory have proved particularly efficient to study lattice-valued maxitive measures, when the target lattice is continuous. Maxitive measures are defined analogously to classical measures with the supremum operation in place of the addition. Building further on the links between domain theory and idempotent analysis highlighted by Lawson ( 2004), we investigate the concept of domain-valued linear forms on an idempotent (semi)module. In addition to proving representation theorems for continuous linear forms, we address two applications: the idempotent Radon-Nikodym theorem and the idempotent Riesz representation theorem. To unify similar results from different mathematical areas, our analysis is carried out in the general Z framework of domain theory.

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Section: A Primer On Z-theory For Continuous Posets and Domainsmentioning

confidence: 99%

What is the role of continuity in continuous linear forms representation?

Poncet

2010

Preprint

View full text Add to dashboard Cite

show abstract

Z-mappings and a classification theorem

Cited by 1 publication

References 5 publications

What is the role of continuity in continuous linear forms representation?

What is the role of continuity in continuous linear forms representation?

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