Insertion and extension theorems for completely distributive lattice valued functions

• Autorzy: García J. G. , Kubiak T.

Identyfikatory

DOI

10.14708/cm.v53i2.801

• Języki publikacji: EN

Abstrakty

EN

Insertion and extension theorems are presented for lattice-valued functions where the lattice is an appropriately based completely distributive lattice endowed with its interval topology.

Słowa kluczowe

EN

lattice; completely distributive; completely join irreducible; ⊲-separable; interval topology; insertion; extension

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol. 53, No. 2
• Strony: 313--319
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

García J. G.

• University of the Basque Country UPV/EHU, Department of Mathematics, Apdo. 644, 48080 Bilbao, Spain

autor

Kubiak T.

• Uniwersytet im. Adama Mickiewicza, Wydział Matematyki i Informatyki, ul. Umultowska 87, 61-614 Poznan, Poland

Bibliografia

• [1] R. Balbes and P. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, 1974.
• [2] R. L. Blair, Extensions of Lebesgue sets and of real valued functions, Czechoslovak Math. J. 31 (1981), 63–74.
• [3] R. L. Blair and M. A. Swardson, Insertion and extension of hedgehog-valued functions, Indian J. Math. 29 (1987), 229–250.
• [4] G. Bossi, J. Gutiérrez García and E. Induráin, Unified representability of total preorders and interval orders through a single function: the lattice approach, Order 26 (2009), 255–275.
• [5] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott, A Compendium on Continuous Lattices, Springer-Verlag, Berlin, 1980.
• [6] L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, New York, 1976.
• [7] J. Gutiérrez García, T. Kubiak and M. A. de Prada Vicente, Insertion of lattice-valued and hedgehog-valued functions, Topology Appl. 153 (2006), 1458–1475.
• [8] J. Gutiérrez García, T. Kubiak and M. A. de Prada Vicente, Controlling disjointness with a hedgehog, Houston J. Math. 35 (2009), 469–484.
• [9] E.P. Lane, A sufficient condition for the insertion of a continuous function, Proc. Amer. Math. Soc. 49 (1975), 90–94.
• [10] E.P. Lane, Insertion of a continuous function, Topology Proc. 4 (1979), 463–478.
• [11] Y.-M. Liu and M.-K. Luo, Lattice-valued Hahn-Dieudonné-Tong theorem and stratification structure, Topology Appl. 45 (1992), 173–188.
• [12] S. Mrówka, On some approximation theorems, Nieuw Archief voor Wiskunde (3) 16 (1968), 94–111.
• [13] D. Papert Strauss, Topological lattices, Proc. London Math. Soc. (3) 18 (1968), 217–230.
• [14] G. N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518–522.