228 research outputs found
Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces
Assuming the existence of certain large cardinal numbers, we prove that for
every projective filter over the set of natural numbers,
-bases in Banach spaces have continuous coordinate functionals. In
particular, this applies to the filter of statistical convergence, thereby we
solve a problem by V. Kadets (at least under the presence of certain large
cardinals). In this setting, we recover also a result of Kochanek who proved
continuity of coordinate functionals for countably generated filters (Studia
Math., 2012).Comment: 10 p
Set Theory
This meeting covered all important aspects of modern Set Theory, including large cardinal theory, combinatorial set theory, descriptive set theory, connections with algebra and analysis, forcing axioms and inner model theory. The presence of an unusually large number (19) of young researchers made the meeting especially dynamic
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