4 papers
Bourgain-uo sequential completeness in vector lattices
Tomasz Kania, JarosÅaw Swaczyna
We revisit Bourgain's 1981 counterexample to the sequential completeness of the `pointwise plus domination' convergence on from the perspective of vector lattices. In this…
Infinite random graphs
Ziemowit Kostana, JarosÅaw Swaczyna, Agnieszka Widz
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, w…
The -property of a Banach space along a filter
Tomasz Kania, JarosÅaw Swaczyna
We examine the analyticity of the class of separable Banach spaces possessing the -property, defined in terms of convergence along a filter. Our results establish that this cla…
Zoo of ideal Schauder basis
Adam Kwela, JarosÅaw Swaczyna
We investigate the notion of filter (equivalently: ideal) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones…