Marek CUTH: Separable determination in Banach spaces
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Abstract: One of the important methods of proofs in the nonseparable Banach space theory is the ``separable reduction''. By a separable reduction we usually mean the possibility to 
extend the validity of a statement from separable spaces to the nonseparable setting without knowing the proof of the statement in the separable case. Experience shows that an optimal 
method of separable reduction is to prove that certain notions are “separably determined”.
During my talk I will present and compare three different approaches to ``separable determination'' - one using the concept of rich families, second via the concept of suitable models 
and third, a new one, using the notion of ω-monotone mappings. I will talk about possible dis/advantages of those approaches and about a recent result which says that in Banach spaces 
all the three are in a sense equivalent.
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