4 citations · 7 across the 12 of their papers we have counts for
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The number of weakly compact convex subsets of the Hilbert space
Antonio Avilés
We prove that for k an uncountable cardinal, there exist 2^k many non homeomorphic weakly compact convex subsets of weight k in the Hilbert space of density k.
Linearly-ordered Radon-Nidkodým compact spaces
Antonio Avilés
We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi…
The unit ball of the Hilbert space in its weak topology
Antonio Avilés
We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce…
Countable products of spaces of finite sets
Antonio Avilés
We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banac…