Geodesic
Sequential convergences in a vector lattice
Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 33-48

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
In the present paper we deal with sequential convergences on a vector lattice $L$ which are compatible with the structure of $L$.
In the present paper we deal with sequential convergences on a vector lattice $L$ which are compatible with the structure of $L$.
DOI : 10.21136/MB.1998.126295
Classification : 46A19, 46A40
Keywords: vector lattice; sequential convergence; archimedean property; Brouwerian lattice 
Jakubík, Ján. Sequential convergences in a vector lattice. Mathematica Bohemica, Tome 123 (1998) no. 1, pp. 33-48. doi: 10.21136/MB.1998.126295
@article{10_21136_MB_1998_126295,
     author = {Jakub{\'\i}k, J\'an},
     title = {Sequential convergences in a vector lattice},
     journal = {Mathematica Bohemica},
     pages = {33--48},
     year = {1998},
     volume = {123},
     number = {1},
     doi = {10.21136/MB.1998.126295},
     mrnumber = {1618711},
     zbl = {0903.46009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126295/}
}
TY  - JOUR
AU  - Jakubík, Ján
TI  - Sequential convergences in a vector lattice
JO  - Mathematica Bohemica
PY  - 1998
SP  - 33
EP  - 48
VL  - 123
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126295/
DO  - 10.21136/MB.1998.126295
LA  - en
ID  - 10_21136_MB_1998_126295
ER  - 
%0 Journal Article
%A Jakubík, Ján
%T Sequential convergences in a vector lattice
%J Mathematica Bohemica
%D 1998
%P 33-48
%V 123
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1998.126295/
%R 10.21136/MB.1998.126295
%G en
%F 10_21136_MB_1998_126295

[1] G. Birkhoff: Lattice Theory. Third edition, Providence, 1967. | MR | Zbl

[2] P. Conrad: Lattice Ordered Groups. Tulane University, 1970. | Zbl

[3] M. Harminc: Sequential convergences on abelian lattice ordered groups. Convergence Structures, Proc. Conf. Bechyně 1984, Mathematical Research 24 (1985), 153-158. | MR

[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

[5] M. Harminc: Sequential convergences on lattice ordered groups. Czechoslovak Math. J. 39 (1989), 232-238. | MR

[6] M. Harminc J. Jakubík: Maximal convergences and minimal proper convergences in l-groups. Czechoslovak Math. J. 39 (1989), 631-640. | MR

[7] J. Jakubík: Convergences and complete distributivity of lattice ordered groups. Math. Slovaca 38 (1988), 269-272. | MR

[8] J. Jakubík: On summability in convergence l-groups. Časopis Pěst. Mat. 113 (1988), 286-292. | MR

[9] J. Jakubík: On some types of kernels of a convergence l-group. Czechoslovak Math. J. 39 (1989), 239-247. | MR

[10] J. Jakubík: Lattice ordered groups having a largest convergence. Czechoslovak Math. J. 39 (1989), 717-729. | MR

[11] J. Jakubík: Sequential convergences in Boolean algebras. Czechoslovak Math. J. 38 (1988), 520-530. | MR

[12] J. Jakubík: Convergences and higher degrees of distributivity in lattice ordered groups and Boolean algebras. Czechoslovak Math. J. 40 (1990), 453-458. | MR

[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 | Zbl

[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

[18] J. Novák: On convergence groups. Czechoslovak Math. J. 20 (1970), 357-374. | MR

[19] B. Z. Vulikh: Introduction to the Theory of Semiordered Spaces. Moskva, 1961. (In Russian.)

Cité par Sources :