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Spaces of Abstract Events |
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| Authors: | Ivan Chajda Helmut Länger |
| Affiliation: | 1. Faculty of Science, Department of Algebra and Geometry, Palacky University Olomouc, 17. listopadu 12, 77146, Olomouc, Czech Republic 2. Faculty of Mathematics and Geoinformation, Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstra?e 8–10, 1040, Vienna, Austria |
| Abstract: | We generalize the concept of a space of numerical events in such a way that this generalization corresponds to arbitrary orthomodular posets whereas spaces of numerical events correspond to orthomodular posets having a full set of states. Moreover, we show that there is a natural one-to-one correspondence between orthomodular posets and certain posets with sectionally antitone involutions. Finally, we characterize orthomodular lattices among orthomodular posets. |
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