Abstract
UDC 519.51
We consider a ballean with an infinite support and a free filter on and define for every and The ballean will be called the <em>ballean-filter mix</em> of and and denoted by It was introduced in [O. V. Petrenko, I. V. Protasov, <em>Balleans and filters</em>, Mat. Stud., <strong>38</strong>, No. 1, 3–11 (2012)] and was used to construction of a non-metrizable Frechet group ballean. In this paper some cardinal invariants are compared. In particular, we give a partial answer to the question: if we mix an ordinal unbounded ballean with a free filter of the subsets of its support, will the mix-structure's density be equal to its capacity, as it holds in the original balleans?
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Reference4 articles.
1. I. V. Protasov, Cellularity and density of balleans, Appl. General Topology, 8, № 2, 283 – 291 (2007), https://doi.org/10.4995/agt.2007.1898
2. O. V. Petrenko, I. V. Protasov, Balleans and filters, Mat. Stud., 38, № 1, 3 – 11 (2012).
3. I. V. Protasov, Coronas of balleans, Topology and Appl., 149, 149 – 160 (2005), https://doi.org/10.1016/j.topol.2004.09.005
4. I. Protasov, M. Zarichnyi, General asymptology, Math. Stud. Monogr. Ser., 12, VNTL Publ., Lviv (2007).