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Keywords:
vector lattice; sequential convergence; archimedean property; Brouwerian lattice
vector lattice; sequential convergence; archimedean property; Brouwerian lattice
Summary:
In the present paper we deal with sequential convergences on a vector lattice $L$ which are compatible with the structure of $L$.
References:
[1] G. Birkhoff: Lattice Theory. Third edition, Providence, 1967. MR 0227053 | Zbl 0153.02501
[2] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. Zbl 0258.06011
[3] M. Harminc: Sequential convergences on abelian lattice ordered groups. Convergence Structures, Proc. Conf. Bechyně 1984, Mathematical Research 24 (1985), 153-158. MR 0835480
[4] M. Harminc: The cardinality of the system of all sequential convergences on an abelian lattice ordered group. Czechoslovak Math. J. 37 (1987), 533-546. MR 0913986
[5] M. Harminc: Sequential convergences on lattice ordered groups. Czechoslovak Math. J. 39 (1989), 232-238. MR 0992130
[6] M. Harminc J. Jakubík: Maximal convergences and minimal proper convergences in l-groups. Czechoslovak Math. J. 39 (1989), 631-640. MR 1017998
[7] J. Jakubík: Convergences and complete distributivity of lattice ordered groups. Math. Slovaca 38 (1988), 269-272. MR 0977905
[8] J. Jakubík: On summability in convergence l-groups. Časopis Pěst. Mat. 113 (1988), 286-292. MR 0960765
[9] J. Jakubík: On some types of kernels of a convergence l-group. Czechoslovak Math. J. 39 (1989), 239-247. MR 0992131
[10] J. Jakubík: Lattice ordered groups having a largest convergence. Czechoslovak Math. J. 39 (1989), 717-729. MR 1018008
[11] J. Jakubík: Sequential convergences in Boolean algebras. Czechoslovak Math. J. 38 (1988), 520-530. MR 0950306
[12] J. Jakubík: Convergences and higher degrees of distributivity in lattice ordered groups and Boolean algebras. Czechoslovak Math. J. 40 (1990), 453-458. MR 1065024
[13] L. V. Kantorovich B. Z. Vulikh A. G. Pinsker: Functional Analysis in Semiordered Spaces. Moskva, 1950. (In Russian.)
[14] S. Leader: Sequential convergence in lattice groups. In: Problems in analysis, Sympos. in Honor of S. Bochner. Princeton Univ. Press, 1970, pp. 273-290. MR 0344842 | Zbl 0212.03703
[15] L. A. Ľusternik V. I. Sobolev: Elements of Functional Analysis. Moskva, 1951. (In Russian.)
[16] W. A. J. Luxemburg A. C. Zaanen: Riesz Spaces. Vol. 1. Amsterdam-London, 1971.
[17] P. Mikusiński: Problems posed at the conference. Proc. Conf. on Convergence, Szczyrk 1979. Katowice 1980, pp. 110-112. MR 0639325
[18] J. Novák: On convergence groups. Czechoslovak Math. J. 20 (1970), 357-374. MR 0263973
[19] B. Z. Vulikh: Introduction to the Theory of Semiordered Spaces. Moskva, 1961. (In Russian.)
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