Mathematica Slovaca | |
Sequential convergences on MV-algebras without Urysohn’s axiom | |
Ján Jakubík1  | |
关键词: MV-algebra; sequential convergence; Urysohn’s axiom; unital lattice-ordered group; | |
DOI : 10.2478/s12175-008-0074-3 | |
学科分类:数学(综合) | |
来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute | |
【 摘 要 】
In a previous author’s paper, sequential convergences on an MV-algebra have been studied; the Urysohn’s axiom was assumed to be valid. The system of all such convergences was denoted by Conv . In the present paper we investigate analogous questions without supposing the validity of the Urysohn’s axiom; the corresponding system of convergences is denoted by conv . Both Conv and conv are partially ordered by the set-theoretical inclusion. We deal with the properties of conv 289-6 and the relations between conv and Conv . We prove that each interval of conv is a distributive lattice. The system conv has the least element, but it does not possess any atom. Hence it is either a singleton set or it is infinite. We consider also the relations between conv and conv G, where (G, u) is a unital lattice-ordered group with = Γ (G, u).
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912080690697ZK.pdf | 197KB | download |