A topology on quantum logics
Sylvia Pulmannová and Zdena Riečanová
Proc. Amer. Math. Soc. 106 (1989), 891-897
Primary 81B10; Secondary 06C15, 54A99
Full-text PDF Free Access
Similar Articles |
Abstract: A uniform topology induced by a set of finite measures on a quantum logic is studied. If is a valuation on , the topology induced by is equivalent to the topology induced by the pseudometric . If the set of measures is large enough, the topology reflects in some sense the structure of : if is a continuous geometry and the measures are totally additive, is weaker than the order topology on . If is atomic, is stronger than . On a separable Hilbert space logic, coincides with the discrete topology. Some cases are found in which .
Beran, Orthomodular lattices, Mathematics and its Applications
(East European Series), D. Reidel Publishing Co., Dordrecht, 1985.
Algebraic approach. MR 784029
Birkgof, Teoriya reshetok, “Nauka”, Moscow, 1984
(Russian). Translated from the English and with an appendix by V. N.
Saliĭ; Translation edited by L. A. Skornyakov. MR 751233
Kalmbach, Orthomodular lattices, London Mathematical Society
Monographs, vol. 18, Academic Press, Inc. [Harcourt Brace Jovanovich,
Publishers], London, 1983. MR 716496
Palko, Topologies on quantum logics induced by measures, Math.
Slovaca 39 (1989), no. 2, 175–189 (English,
with Russian summary). MR 1018259
Riečanová, Topology in a quantum logic induced by a
measure, Proceedings of the Conference: Topology and Measure, V (Binz,
1987), Wissensch. Beitr., Ernst-Moritz-Arndt Univ., Greifswald, 1988,
pp. 126–130. MR 1029570
T. A. Sarymsakov, S. A. Ajupov, Z. Chadžijev, and V. J. čilin, Uporiadočennije algebry, Taškent, "FAN" 1983.
S. Varadarajan, Geometry of quantum theory, 2nd ed.,
Springer-Verlag, New York, 1985. MR 805158
- L. Beran, Orthomodular lattices, Academia-Reidel P.C., Dordrecht, Holland 1984. MR 784029 (86m:06015b)
- G. Birkhoff, Lattice theory (Russian translation: Teorija rešetok), Moscow, "NAUKA", 1984. MR 751233 (85e:06001)
- G. Kalmbach, Orthomodular lattices, Academic Press, London 1983. MR 716496 (85f:06012)
- V. Palko, Topologies on quantum logics induced by measures, Math. Slovaca, to appear. MR 1018259 (90i:03071)
- Z. Riečanová, Topology in a quantum logic induced by a measure, Proceedings of the Conf. "Topology and Measure V", Wissenschaftliche Beitrage der EMA-Univesität Greifswald DDR, Greifswald 1988. MR 1029570 (91b:81015)
- T. A. Sarymsakov, S. A. Ajupov, Z. Chadžijev, and V. J. čilin, Uporiadočennije algebry, Taškent, "FAN" 1983.
- V. S. Varadarajan, Geometry of quantum theory, Springer-Verlag, New York 1985. MR 805158 (87a:81009)
Retrieve articles in Proceedings of the American Mathematical Society
Retrieve articles in all journals
uniform topology generated by measures
© Copyright 1989
American Mathematical Society