| Title:
|
Sequential convergences in a vector lattice (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
33-48 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we deal with sequential convergences on a vector lattice $L$ which are compatible with the structure of $L$. (English) |
| Keyword:
|
vector lattice |
| Keyword:
|
sequential convergence |
| Keyword:
|
archimedean property |
| Keyword:
|
Brouwerian lattice |
| MSC:
|
46A19 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 0903.46009 |
| idMR:
|
MR1618711 |
| DOI:
|
10.21136/MB.1998.126295 |
| . |
| Date available:
|
2009-09-24T21:29:00Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126295 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory.Third edition, Providence, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[2] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[3] M. Harminc: Sequential convergences on abelian lattice ordered groups.Convergence Structures, Proc. Conf. Bechyně 1984, Mathematical Research 24 (1985), 153-158. MR 0835480 |
| Reference:
|
[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 |
| Reference:
|
[5] M. Harminc: Sequential convergences on lattice ordered groups.Czechoslovak Math. J. 39 (1989), 232-238. MR 0992130 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] J. Jakubík: On some types of kernels of a convergence l-group.Czechoslovak Math. J. 39 (1989), 239-247. MR 0992131 |
| Reference:
|
[10] J. Jakubík: Lattice ordered groups having a largest convergence.Czechoslovak Math. J. 39 (1989), 717-729. MR 1018008 |
| Reference:
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[11] J. Jakubík: Sequential convergences in Boolean algebras.Czechoslovak Math. J. 38 (1988), 520-530. MR 0950306 |
| Reference:
|
[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 |
| Reference:
|
[13] L. V. Kantorovich B. Z. Vulikh A. G. Pinsker: Functional Analysis in Semiordered Spaces.Moskva, 1950. (In Russian.) |
| Reference:
|
[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. Zbl 0212.03703, MR 0344842 |
| Reference:
|
[15] L. A. Ľusternik V. I. Sobolev: Elements of Functional Analysis.Moskva, 1951. (In Russian.) |
| Reference:
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[16] W. A. J. Luxemburg A. C. Zaanen: Riesz Spaces.Vol. 1. Amsterdam-London, 1971. |
| Reference:
|
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| Reference:
|
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| Reference:
|
[19] B. Z. Vulikh: Introduction to the Theory of Semiordered Spaces.Moskva, 1961. (In Russian.) |
| . |
