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We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikodým compacta.
This survey’s first object is to introduce the reader to Lindelöf Σ-spaces; since the author would like this introduction to be useful for postgraduate students and non-specialists in the area, most of the basic results are given with complete proofs. The second object is to make an overview of the recent progress achieved in the study of Lindelöf Σ-spaces. Several popular topics are presented together...
We study splittability over some classes of compact spaces which are useful in functional analysis and general topology. Among other things we show that a scattered pseudocompact space splittable over the class of Eberlein compact spaces is Eberlein compact. We also prove that a compact space splittable over the class of Eberlein compact spaces is hereditarily $$\sigma $$ σ -metacompact,...
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