Convergence structures induced by scales

Topology and its Applications

Volumn 73, Issue 3, 1996, Pages 267-284

  Erné, Marcel ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

(Bi )algebraic lattice; Content; Continuous; Measure; Order convergence; Order topology; Orthomodular lattice; Scale; Valuation

Indexed keywords

EID: 15844406215     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(96)00074-0     Document Type: Article

References (22)

1. G. Birkhoff, Lattice Theory, 3rd ed., Amer. Math. Soc. Coll. Publ. 25 (American Mathematical Society, Providence, RI, 1973).
2. T.H. Choe and R.J. Greechie, Profinite orthomodular lattices, Preprint, McMaster University, Hamilton, and Kansas State University, Manhattan (1990).
3. M. Erné, Order-topological lattices, Glasgow Math. J. 21 (1980) 57-68.
4. M. Erné, Topologies on products of partially ordered sets III, Algebra Universalis 13 (1981) 1-23.
5. M. Erné, On the existence of decompositions in lattices, Algebra Universalis 16 (1983) 338-343.
6. M. Erné, Lattice topologies with interval bases, Preprint, Universität Hannover (1993).
7. M. Erné, Continuous lattice operations, Preprint, Universität Hannover (1993).
8. M. Erné and S. Week, Order convergence in lattices, Rocky Mountain J. Math. 10 (1980) 805-818.
9. M. Erné and H. Gatzke, Convergence and continuity in partially ordered sets and semilattices, in: R.-E. Hoffmann and K.H. Hofmann, eds., Continuous Lattices and Their Applications, Bremen 1982, Lecture Notes in Pure and Appl. Math. 109 (Marcel Dekker, New York, 1985) 9-40.
10. M. Erne and Z. Riečanová, Order-topological complete orthomodular lattices, Topology Appl. 61 (1995) 215-227.
11. G. Grätzer, General Lattice Theory (Birkhäuser, Basel, 1973).
12. G. Kalmbach, Orthomodular Lattices (Academic Press, London, 1983).
13. J. Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math. 61 (1955) 524-541.
14. D.C. Kent, On the order topology in a lattice, Illinois J. Math. 10 (1966) 90-96.
15. S. Pulmannová and Z. Riečanová, A topology on quantum logics, Proc. Amer. Math. Soc. 106 (1989) 891-897.
16. S. Pulmannová and Z. Riečanová, Logics with separating sets of measures, Math. Slovaca 41 (1991) 167-177.
17. S. Pulmannová and Z. Riečanová, Compact topological orthomodular lattices, in; Contributions to General Algebra 7 (Hölder-Pichler-Tempsky, Wien, 1991) 277-282.
18. Z. Riečanová, Topologies in atomic quantum logics, Acta Univ. Carolin. Math. Phys. 30 (1989) 143-148.
19. Z. Riečanová, Measures and topologies on atomic quantum logics, in: Mathematical Research 66, Topology, Measures and Fractals (Akademie-Verlag, 1992) 154-161.
20. Z. Riečanová, Applications of topological methods to the completion of atomic orthomodular lattices, Demonstratio Mathematica 24 (1991) 331-341.
21. T.A. Sarymsakov, S.A. Ajupov, Z. Chadžijev and V.J. Čilin, Uporiadočennyje Algebry (FAN, Taškent, 1983).
22. D.A. Vladimirov, Boolesche Algebren (Akademie-Verlag, Berlin, 1972).