| Title:
|
Modular functions on multilattices (English) |
| Author:
|
Avallone, Anna |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
499-512 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $L$. (English) |
| Keyword:
|
multilattices |
| Keyword:
|
modular functions |
| MSC:
|
06B99 |
| MSC:
|
28B10 |
| idZBL:
|
Zbl 1011.28008 |
| idMR:
|
MR1923256 |
| . |
| Date available:
|
2009-09-24T10:53:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127738 |
| . |
| Reference:
|
[1] A. Avallone: Liapunov theorem for modular functions.Internat. J. Theoret. Phys. 34 (1995), 1197–1204. Zbl 0841.28007, MR 1353662, 10.1007/BF00676229 |
| Reference:
|
[2] A. Avallone: Nonatomic vector-valued modular functions.Annal. Soc. Math. Polon. Series I: Comment. Math. XXXIX (1999), 37–50. Zbl 0987.28012, MR 1739014 |
| Reference:
|
[3] A. Avallone, G. Barbieri and R. Cilia: Control and separating points of modular functions.Math. Slovaca 43 (1999), . MR 1696950 |
| Reference:
|
[4] A. Avallone and A. De Simone: Extensions of modular functions on orthomodular lattices.Italian J. Pure Appl. Math, To appear. MR 1842373 |
| Reference:
|
[5] A. Avallone and M. A. Lepellere: Modular functions: Uniform boundedness and compactness.Rend. Circ. Mat. Palermo XLVII (1998), 221–264. MR 1633479 |
| Reference:
|
[6] A. Avallone and J. Hamhalter: Extension theorems (vector measures on quantum logics).Czechoslovak Math. J. 46 (121) (1996), 179–192. MR 1371699 |
| Reference:
|
[7] A. Avallone and H. Weber: Lattice uniformities generated by filters.J. Math. Anal. Appl. 209 (1997), 507–528. MR 1474622, 10.1006/jmaa.1996.5291 |
| Reference:
|
[8] G. Barbieri and H. Weber: A topological approach to the study of fuzzy measures.Funct. Anal. Econom. Theory, Springer, 1998, pp. 17–46. MR 1730117 |
| Reference:
|
[9] G. Barbieri, M. A. Lepellere and H. Weber: The Hahn decomposition theorem and applications.Fuzzy Sets Systems 118 (2001), 519–528. MR 1809398 |
| Reference:
|
[10] H. J. Bandelt, M. Van de Vel and E. Verheul: Modular interval spaces.Math. Nachr. 163 (1993), 177–201. MR 1235066, 10.1002/mana.19931630117 |
| Reference:
|
[11] M. Benado: Les ensembles partiellement ordonnes et le theoreme de raffinement de Schrelier II.Czechoslovak Math. J. 5 (1955), 308–344. MR 0076744 |
| Reference:
|
[12] G. Birkhoff: Lattice Theory, Third edition.AMS Providence, R.I., 1967. MR 0227053 |
| Reference:
|
[13] I. Fleischer and T. Traynor: Equivalence of group-valued measure on an abstract lattice.Bull. Acad. Pol. Sci. 28 (1980), 549–556. MR 0628641 |
| Reference:
|
[14] I. Fleischer and T. Traynor: Group-valued modular functions.Algebra Universalis 14 (1982), 287–291. MR 0654397, 10.1007/BF02483932 |
| Reference:
|
[15] M. G. Graziano: Uniformities of Fréchet-Nikodým type on Vitali spaces.Semigroup Forum 61 (2000), 91–115. Zbl 0966.28008, MR 1839217, 10.1007/PL00006017 |
| Reference:
|
[16] D. J. Hensen: An axiomatic characterization of multilattices.Discrete Math. 33 (1981), 99–101. MR 0597233, 10.1016/0012-365X(81)90263-6 |
| Reference:
|
[17] J. Jakubík: Sur les axiomes des multistructures.Czechoslovak Math. J. 6 (1956), 426–430. MR 0099933 |
| Reference:
|
[18] J. Jakubík and M. Kolibiar: Isometries of multilattice groups.Czechoslovak Math. J. 33 (1983), 602–612. MR 0721089 |
| Reference:
|
[19] J. Lihová: Valuations and distance function on directed multilattices.Math. Slovaca 46 (1996), 143–155. MR 1426999 |
| Reference:
|
[20] J. Lihová and K. Repasky: Congruence relations on and varieties of directed multilattices.Math. Slovaca 38 (1988), 105–122. MR 0945364 |
| Reference:
|
[21] T. Traynor: Modular functions and their Fréchet-Nikodým topologies.Lectures Notes in Math. 1089 (1984), 171–180. Zbl 0576.28014, MR 0786696, 10.1007/BFb0072613 |
| Reference:
|
[22] H. Weber: Uniform Lattices I: A generalization of topological Riesz space and topological Boolean rings; Uniform lattices II.Ann. Mat. Pura Appl. 160 (1991), 347–370. MR 1163215, 10.1007/BF01764134 |
| Reference:
|
[23] H. Weber: Lattice uniformities and modular functions on orthomodular lattices.Order 12 (1995), 295–305. Zbl 0834.06013, MR 1361614, 10.1007/BF01111744 |
| Reference:
|
[24] H. Weber: On modular functions.Funct. Approx. XXIV (1996), 35–52. Zbl 0887.06011, MR 1453447 |
| Reference:
|
[25] H. Weber: Valuations on complemented lattices.Internat. J. Theoret. Phys. 34 (1995), 1799–1806. Zbl 0843.06005, MR 1353726, 10.1007/BF00676294 |
| Reference:
|
[26] H. Weber: Complemented uniform lattices.Topology Appl. 105 (2000), 47–64. Zbl 1121.54312, MR 1761086, 10.1016/S0166-8641(99)00049-8 |
| Reference:
|
[27] H. Weber: Two extension theorems. Modular functions on complemented lattices.Preprint. Zbl 0998.06006, MR 1885457 |
| . |
