Objective
In this project we propose to use set-theoretic methods in order to study two sets of problems coming from functional analysis. The first concerns with the problem of the continuous images of Radon-Nikodym compact spaces posed by Namioka some thirty years ago. This class of compacta has been isolated in the early 1970 and apos;s in the course of studying a Radon-Nikodym property of vector measures. Particularly useful was the characterization in terms of Frechet differentiability leading to a purely topological formulation of the problem. The other is the problem of the uniform regularity of Borel measures, posed by Pol for Rosenthal compacta and by Fremlin for general first countable compacta (it is one prominent item of his famous list of problems).
We plan to supplement the standard techniques in dealing with this kind of problems with advanced methods of set theory and Ramsey theory, and particularly the method of forcing. It is generally believed that one of the reasons why these problems have been open for so long time is the fact that so far too elementary set-theoretic methods have been applied. During the last thirty or forty years set theory has advanced considerably and specially its method of forcing invented by Paul J. Cohen some forty years ago in order to prove the independence of the Continuum Hypothesis. By now this method has been developed to the point of being able to obtain results that are not necessarily consistency results.
Moreover in recent times this method has been successfully merged with another powerful method, the Ramsey-theoretic method. We hope that the combination of these two methods is likely to give us a substantial progress on these two long- standing open problems of functional analysis.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics mathematical analysis functional analysis
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Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2005-MOBILITY-5
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Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
BVRI PARIS
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.