Maximal convergences and minimal proper convergences in ℓ -groups

Matúš Harminc; Ján Jakubík

Czechoslovak Mathematical Journal (1989)

  • Volume: 39, Issue: 4, page 631-640
  • ISSN: 0011-4642

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Harminc, Matúš, and Jakubík, Ján. "Maximal convergences and minimal proper convergences in $\ell $-groups." Czechoslovak Mathematical Journal 39.4 (1989): 631-640. <http://eudml.org/doc/13812>.

@article{Harminc1989,
author = {Harminc, Matúš, Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {convergence; lattice ordered group; direct product; atoms},
language = {eng},
number = {4},
pages = {631-640},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximal convergences and minimal proper convergences in $\ell $-groups},
url = {http://eudml.org/doc/13812},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Harminc, Matúš
AU - Jakubík, Ján
TI - Maximal convergences and minimal proper convergences in $\ell $-groups
JO - Czechoslovak Mathematical Journal
PY - 1989
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 4
SP - 631
EP - 640
LA - eng
KW - convergence; lattice ordered group; direct product; atoms
UR - http://eudml.org/doc/13812
ER -

References

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  1. G. Birkhoff, Lattice theory, Third edition, Providence, 1967. (1967) Zbl0153.02501MR0227053
  2. A. Bigard K. Keimel S. Wolfenstein, Groupes et Anneaux Réticulés, Lecture Notes in Math., No. 608, Springer-Verlag, Berlin-Heidelberg-New York, 1977. (1977) MR0552653
  3. P. F. Conrad, Lattice-ordered groups, Tulane University, 1970. (1970) Zbl0258.06011
  4. D. Dikranjan R. Frič F. Zanolin, On convergence groups with dense coarse subgroups, Czechoslovak Math. J. 37, 1987, 471-479. (1987) MR0904771
  5. D. Doitchinov, Produits de groupes topologiques minimaux, Bull. Sci. Math. 97, 1972, 59-64. (1972) Zbl0236.22002MR0308323
  6. С. J. Everett S. Ulam, 10.1090/S0002-9947-1945-0012285-5, Trans. Amer. Math. Soc. 57, 1945, 208-216. (1945) MR0012285DOI10.1090/S0002-9947-1945-0012285-5
  7. R. Frič, Products of coarse convergence groups, Czechoslovak Math. J. 38, 1988, 285-290. (1988) MR0946298
  8. M. Harminc, Sequential convergences on abelian lattice ordered groups, Convergence structures 1984. Mathematical Research, Band 24, Akademie-Verlag, Berlin, 1985, 153-158. (1984) MR0835480
  9. M. Harminc, Convergences on lattice ordered groups, Dissertation, Math. Inst. Acad. Sci., Bratislava, 1986. (In Slovak.) (1986) 
  10. M. Harminc, Cardinality of the system of all sequential convergences on an abelian lattice ordered group, Czechoslovak Math. J. 37, 1987, 533-546. (1987) Zbl0645.06006MR0913986
  11. M. Harminc, Sequential convergences on lattice ordered groups, Czechoslovak Math. J. 39, 1989, 232-238. (1989) MR0992130
  12. J. Jakubík, On summability in convergence l -groups, Čas. pěst. mat. 113, 1988, 286-292. (1988) MR0960765
  13. J. Jakubík, Lattice ordered groups having a largest convergence, Czechoslov. Math. J. 39, 1989, 717-729. (1989) MR1018008
  14. J. Jakubík, Convergences and complete distributivity of lattice ordered groups, Math. Slovaca 38, 1988, 269-272. (1988) MR0977905
  15. P. Mikusiński, Problems posed at the conference, Proc. Conf. on Convergence, Szczyrk 1979, Katowice 1980, 110-112. (1979) MR0639325
  16. E. Pap, Funkcionalna analiza, nizovne konvergenciji, neki principi funkcionalne analize, Novi Sad, 1982. (1982) MR0683763
  17. F. Papangelou, 10.1007/BF01344076, Math. Ann. 155, 1964, 81-107. (1964) MR0174498DOI10.1007/BF01344076

Citations in EuDML Documents

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  1. Ján Jakubík, Convergence l -groups with zero radical
  2. Ján Jakubík, Sequential convergences in distributive lattices
  3. Ján Jakubík, Principal convergences on lattice ordered groups
  4. Ján Jakubík, Sequential convergences on free lattice ordered groups
  5. Ján Jakubík, Sequential convergences in ℓ -groups without Urysohn’s axiom
  6. Ján Jakubík, Sequential convergences in a vector lattice
  7. Ján Jakubík, Convergences on lattice ordered groups with a finite number of disjoint elements

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