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Scott convergence and fuzzy Scott topology onL-posets

100%

Liu H., Chen L.

Open Mathematics

2017

tom 15

nr 1

815-827

We firstly generalize the fuzzy way-below relation on an L-poset, and consider its continuity by means of this relation. After that, we introduce a kind of stratified L-generalized convergence structure on an L-poset. In terms of that, L-fuzzy Scott topology and fuzzy Scott topology are considered, and the properties of fuzzy Scott topology are discussed in detail. At last, we investigate the Scott convergence of stratified L-filters on an L-poset, and show that an L-poset is continuous if and only if the Scott convergence on it coincides with the convergence with respect to the corresponding topological space.

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Decomposition of topologies on lattices and hyperspaces

46%

Costantini C., Vitolo P.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction.................................................................................5 1. Decomposable topologies.......................................................6 2. Locally convex topologies......................................................10 3. Semilattices. Strong decomposability.....................................13 4. Convex topologies.................................................................15 5. Topologies on linearly ordered sets.......................................18 6. Topologies on lattices............................................................20 7. The Scott topology.................................................................26 8. Uniqueness of decomposition................................................28 9. Hyperspace topologies..........................................................32 10. The Vietoris topology...........................................................35 11. The Hausdorff metric topology.............................................37 12. The proximal topology..........................................................39 13. The Kuratowski convergence..............................................40 14. Uniqueness of decomposition for hypertopologies..............44 References................................................................................47

Ograniczanie wyników

1 Open Mathematics

1 Chen L.

1 Costantini C.

1 Liu H.

1 Vitolo P.

1 2017

1 1999

Wyniki wyszukiwania

Scott convergence and fuzzy Scott topology onL-posets

Decomposition of topologies on lattices and hyperspaces