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Topological and order-topological orthomodular lattices
| Content Provider | Scilit |
|---|---|
| Author | Riecanová, Zdenka |
| Copyright Year | 1992 |
| Description | The necessary and sufficient conditions for atomic orthomodular lattices to have the MacNeille completion modular, or (o)-continuous or order topological, orthomodular lattices are proved. Moreover we show that if in an orthomodular lattice the (o)-convergence of filters is topological then the (o)-convergence of nets need not be topological. Finally we show that even in the case when the MacNeille completion of an orthomodular lattice L is order-topological, then in general the (o)-convergence of nets in does not imply their (o)-convergence in L. (This disproves, also for the orthomodular and order-topological case, one statement in G.Birkhoff's book.) |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5E406BB071DFD566EE69DDDC9D7666EF/S0004972700012168a.pdf/div-class-title-topological-and-order-topological-orthomodular-lattices-div.pdf |
| Ending Page | 518 |
| Page Count | 10 |
| Starting Page | 509 |
| ISSN | 00049727 |
| e-ISSN | 17551633 |
| DOI | 10.1017/s0004972700012168 |
| Journal | Bulletin of the Australian Mathematical Society |
| Issue Number | 3 |
| Volume Number | 46 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1992-12-01 |
| Access Restriction | Open |
| Subject Keyword | Bulletin of the Australian Mathematical Society Applied Mathematics Orthomodular Lattices Order Topological Orthomodular |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
