Pathology of submeasures and $$F_{\sigma }$$ ideals
Copyright policy )Pathology of submeasures and $$F_{\sigma }$$ ideals
AbstractWe address some phenomena about the interaction between lower semicontinuous submeasures on $${\mathbb {N}}$$ N and $$F_{\sigma }$$ F σ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological $$F_{\sigma }$$ F σ ideals. We give a partial answers to the question of whether every nonpathological tall $$F_{\sigma }$$ F σ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological $$F_{\sigma }$$ F σ ideals using sequences in Banach spaces.
Theory of Banach Spaces and Operators, Study of properties and structures of commutative rings, tall ideal, Borel selectors, Quantum mechanics, perfectly bounded sets, Katětov order, nonpathological submeasure, FOS: Mathematics, Mathematical Physics, Mathematics - General Topology, Model Theory and Topological Dynamics, Algebra over a field, Algebra and Number Theory, Physics, Pure mathematics, Mathematics - Logic, Sigma, Mathematics - Functional Analysis, Topological Dynamics, Convergence and divergence of series and sequences, Physical Sciences, Idealization, Geometry and Topology, \(F_{\sigma}\) ideal, Descriptive set theory, Mathematics
Theory of Banach Spaces and Operators, Study of properties and structures of commutative rings, tall ideal, Borel selectors, Quantum mechanics, perfectly bounded sets, Katětov order, nonpathological submeasure, FOS: Mathematics, Mathematical Physics, Mathematics - General Topology, Model Theory and Topological Dynamics, Algebra over a field, Algebra and Number Theory, Physics, Pure mathematics, Mathematics - Logic, Sigma, Mathematics - Functional Analysis, Topological Dynamics, Convergence and divergence of series and sequences, Physical Sciences, Idealization, Geometry and Topology, \(F_{\sigma}\) ideal, Descriptive set theory, Mathematics
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