Density and capacity of balleans generated by filters
UDC 519.51 We consider a ballean $\mathbb B=(X,P,B)$ with an infinite support $X$ and a free filter $\phi$ on $X$ and define $B_{P\times\phi}(x,(\alpha,F))$ for every $\alpha\in P$ and $F\in \phi.$ The ballean $(X,P\times\phi, B_{P\times\phi})$ will be called the ballean-filter mix of $\mathbb B$ an...
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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/648 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 519.51
We consider a ballean $\mathbb B=(X,P,B)$ with an infinite support $X$ and a free filter $\phi$ on $X$ and define $B_{P\times\phi}(x,(\alpha,F))$ for every $\alpha\in P$ and $F\in \phi.$ The ballean $(X,P\times\phi, B_{P\times\phi})$ will be called the ballean-filter mix of $\mathbb B$ and $\phi$ and denoted by $\mathbb B(B,\phi).$ It was introduced in [O. V. Petrenko, I. V. Protasov, Balleans and filters, Mat. Stud., 38, 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? |
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| DOI: | 10.37863/umzh.v73i4.648 |