We consider a ballean 𝔹 = (X, P,B) with an infinite support X and a free filter 𝜙 on X and define BP×𝜙(x, (𝛼, F)) for every 𝛼 𝜖 P and F 𝜖 𝜙. The ballean (X, P×𝜙, BP×𝜙) is called a ballean-filter mix of 𝔹 and 𝜙 and denoted by 𝔹(B, 𝜙). It was introduced by O. Petrenko and I. Protasov in [Mat. Stud., 38, No. 1, 3–11 (2012)] and used to construct a nonmetrizable ballean of the Fréchet group. We compare some cardinal invariants. In particular, we give a partial answer to the following question: If we mix an ordinal unbounded ballean with a free filter of the subsets of its support, then is it true that the density of mix structure is equal to its capacity, as in the case of the original balleans?
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I. V. Protasov, “Cellularity and density of balleans,” Appl. Gen. Topol., 8, No. 2, 283–291 (2007).
O. V. Petrenko and I. V. Protasov, “Balleans and filters,” Mat. Stud., 38, No. 1, 3–11 (2012).
I. V. Protasov, “Coronas of balleans,” Topol. Appl., 149, 149–160 (2005).
I. Protasov and M. Zarichnyi, “General asymptology,” Math. Stud. Monogr. Ser., 12, VNTL Publ., Lviv (2007).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 4, pp. 467–473, April, 2021. Ukrainian DOI: 10.37863/umzh.v73i4.648.
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Brzeska, A. Density and Capacity of Balleans Generated By Filters. Ukr Math J 73, 547–555 (2021). https://doi.org/10.1007/s11253-021-01942-x
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DOI: https://doi.org/10.1007/s11253-021-01942-x