Modular functions on multilattices

Anna Avallone

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 3, page 499-512
  • ISSN: 0011-4642

Abstract

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We prove that every modular function on a multilattice L with values in a topological Abelian group generates a uniformity on L which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of L .

How to cite

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Avallone, Anna. "Modular functions on multilattices." Czechoslovak Mathematical Journal 52.3 (2002): 499-512. <http://eudml.org/doc/30719>.

@article{Avallone2002,
abstract = {We prove that every modular function on a multilattice $L$ with values in a topological Abelian group generates a uniformity on $L$ which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of $L$.},
author = {Avallone, Anna},
journal = {Czechoslovak Mathematical Journal},
keywords = {multilattices; modular functions; multilattices; modular functions},
language = {eng},
number = {3},
pages = {499-512},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modular functions on multilattices},
url = {http://eudml.org/doc/30719},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Avallone, Anna
TI - Modular functions on multilattices
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 3
SP - 499
EP - 512
AB - We prove that every modular function on a multilattice $L$ with values in a topological Abelian group generates a uniformity on $L$ which makes the multilattice operations uniformly continuous with respect to the exponential uniformity on the power set of $L$.
LA - eng
KW - multilattices; modular functions; multilattices; modular functions
UR - http://eudml.org/doc/30719
ER -

References

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  1. 10.1007/BF00676229, Internat. J.  Theoret. Phys. 34 (1995), 1197–1204. (1995) Zbl0841.28007MR1353662DOI10.1007/BF00676229
  2. Nonatomic vector-valued modular functions, Annal. Soc. Math. Polon. Series I: Comment. Math. XXXIX (1999), 37–50. (1999) Zbl0987.28012MR1739014
  3. Control and separating points of modular functions, Math. Slovaca 43 (1999), . (1999) MR1696950
  4. Extensions of modular functions on orthomodular lattices, Italian J. Pure Appl. Math, To appear. MR1842373
  5. Modular functions: Uniform boundedness and compactness, Rend. Circ. Mat. Palermo XLVII (1998), 221–264. (1998) MR1633479
  6. Extension theorems (vector measures on quantum logics), Czechoslovak Math. J.  46 (121) (1996), 179–192. (1996) MR1371699
  7. 10.1006/jmaa.1996.5291, J.  Math. Anal. Appl. 209 (1997), 507–528. (1997) MR1474622DOI10.1006/jmaa.1996.5291
  8. A topological approach to the study of fuzzy measures, Funct. Anal. Econom. Theory, Springer, 1998, pp. 17–46. (1998) MR1730117
  9. The Hahn decomposition theorem and applications, Fuzzy Sets Systems 118 (2001), 519–528. (2001) MR1809398
  10. 10.1002/mana.19931630117, Math. Nachr. 163 (1993), 177–201. (1993) MR1235066DOI10.1002/mana.19931630117
  11. Les ensembles partiellement ordonnes et le theoreme de raffinement de Schrelier II, Czechoslovak Math.  J. 5 (1955), 308–344. (1955) MR0076744
  12. Lattice Theory, Third edition, AMS Providence, R.I., 1967. (1967) MR0227053
  13. Equivalence of group-valued measure on an abstract lattice, Bull. Acad. Pol. Sci. 28 (1980), 549–556. (1980) MR0628641
  14. 10.1007/BF02483932, Algebra Universalis 14 (1982), 287–291. (1982) MR0654397DOI10.1007/BF02483932
  15. 10.1007/PL00006017, Semigroup Forum 61 (2000), 91–115. (2000) Zbl0966.28008MR1839217DOI10.1007/PL00006017
  16. 10.1016/0012-365X(81)90263-6, Discrete Math. 33 (1981), 99–101. (1981) MR0597233DOI10.1016/0012-365X(81)90263-6
  17. Sur les axiomes des multistructures, Czechoslovak Math.  J. 6 (1956), 426–430. (1956) MR0099933
  18. Isometries of multilattice groups, Czechoslovak Math.  J. 33 (1983), 602–612. (1983) MR0721089
  19. Valuations and distance function on directed multilattices, Math. Slovaca 46 (1996), 143–155. (1996) MR1426999
  20. Congruence relations on and varieties of directed multilattices, Math. Slovaca 38 (1988), 105–122. (1988) MR0945364
  21. 10.1007/BFb0072613, Lectures Notes in  Math. 1089 (1984), 171–180. (1984) Zbl0576.28014MR0786696DOI10.1007/BFb0072613
  22. 10.1007/BF01764134, Ann. Mat. Pura Appl. 160 (1991), 347–370. (1991) MR1163215DOI10.1007/BF01764134
  23. 10.1007/BF01111744, Order 12 (1995), 295–305. (1995) Zbl0834.06013MR1361614DOI10.1007/BF01111744
  24. On modular functions, Funct. Approx. XXIV (1996), 35–52. (1996) Zbl0887.06011MR1453447
  25. 10.1007/BF00676294, Internat. J.  Theoret. Phys. 34 (1995), 1799–1806. (1995) Zbl0843.06005MR1353726DOI10.1007/BF00676294
  26. 10.1016/S0166-8641(99)00049-8, Topology Appl. 105 (2000), 47–64. (2000) Zbl1121.54312MR1761086DOI10.1016/S0166-8641(99)00049-8
  27. Two extension theorems. Modular functions on complemented lattices, Preprint. Zbl0998.06006MR1885457

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