1 citations · 1 across the 10 of their papers we have counts for
12 papers
On almost disjoint families and Johnson-Lindenstrauss spaces
Antonio Avilés, Grzegorz Plebanek, Luis Sáenz
Every almost disjoint family of infinite subsets of gives rise to a scattered compact space and a family of Johnson-Lindenstrauss spaces JL. We consider almost…
The ball fixed point property in spaces of continuous functions
Antonio Avilés, María Japón, Christopher Lennard +2
A Banach space has the ball fixed point property (BFPP) if for every closed ball and for every nonexpansive mapping , there is a fixed point. We study the B…
A Banach space with -orthogonal sequences but without -orthogonal elements
Antonio Avilés, Gonzalo Martínez-Cervantes, Alejandro Poveda +1
We prove that the existence of Banach spaces with -orthogonal sequences but without -orthogonal elements is independent of the standard foundation of Mathematics, ZFC. This p…
Every Lindelöf scattered subspace of a -product of real lines is -compact
Antonio Avilés, Mikołaj Krupski
We prove that every Lindelöf scattered subspace of a -product of first-countable spaces is -compact. In particular, we obtain the result stated in the title. This answers som…
On the class of NY compact spaces of finitely supported elements and related classes
Antonio Avilés, Mikołaj Krupski
We prove that a compact space embeds into a -product of compact metrizable spaces (-product of intervals) if and only if is (strongly countable-dimensional) hereditar…
Coordinate systems in Banach spaces and lattices
Antonio Avilés, Christian Rosendal, Mitchell A. Taylor +1
Using methods of descriptive set theory, in particular, the determinacy of infinite games of perfect information, we answer several questions from the literature regarding differen…
Barely alternating real almost chains and extension operators for compact lines
Antonio Avilés, Maciej Korpalski
Assume . We show that for every real chain of size in the quotient Boolean algebra we can find an almost chain of representatives such that every $n\in…
Atomicity of Boolean algebras and vector lattices in terms of order convergence
Antonio Avilés, Eugene Bilokopytov, Vladimir G. Troitsky
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an A…
Some examples concerning and metrizably fibered compacta
Antonio Avilés, Mikołaj Krupski
The class of -spaces was introduced in 2006 by Kubiś, Okunev and Szeptycki as a natural refinement of the classical and important notion of Lindelöf -spaces. Compact…
Topological properties in tensor products of Banach spaces
Antonio Avilés, Gonzalo Martínez-Cervantes, José Rodríguez +1
Given two Banach spaces and , we analyze when the projective tensor product has Corson's property (C) or is weakly Lindelöf determined (WLD), subspac…
Banach spaces containing and elements in the fourth dual
Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca
A recent result of T.~Abrahamsen, P.~Hájek and S.~Troyanski states that a separable Banach space is almost square if and only if there exists such that $\|x+h\|…
The McShane integral in weakly compactly generated spaces
Antonio Avilés, Grzegorz Plebanek, José Rodríguez
Di Piazza and Preiss asked whether every Pettis integrable function defined on [0,1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this p…