Continuous Flames and Countably Approximating Frames

  • Published : 2000.12.01

Abstract

This paper is a sequel to [24]. It is well known that the order structure plays the important role in the study of various mathematical structures. In 1972, Scott has introduced a concept of continuous lattices and has shown the equivalence between continuous lattices and injective $T_0-spaces$. There have been many efforts made to generalize continuous lattices and extend corresponding properties to them. We introduce another class of frames, namely countably approximating frames, generalizing continuous frames and study its basic properties.

Keywords

References

  1. Stone Space Johnstone, P.T.
  2. Ann. Math. v.3a Lattices and topological spaces Wallman, H.
  3. Lect. Notes in Math. v.871 Coherent frames Banaschewski, B.
  4. Lect. Notes in Math. v.871 Continuous posets, prime spectra of completely distributive complete lattices, and Hausdorff compactifications Hoffmann, R.-E.
  5. Lect. Notes in Math. v.274 Continuous lattices Scott, D.S.
  6. Festschrift Techn. Hoch. Braunschweig;Ges. Werke v.Ⅱ $\"{U}$ber Zerlegungen von Zahlen durch ihre gr$\"{o}$ssten gemeinsamen Teiler Dedekind, R.
  7. A Compendium of Continuous Lattices Gierz, G.;K.H. Hofmann;K. Keimel;J.D. Lawson;M. Mislove;D.S. Scott
  8. Universal Algebra Gr$\"{a}$tzer, G.
  9. J. London Math. Soc. v.2 Topological semilattices with small semilattices Lawson, J.D.
  10. Math. Proc. Cambridge Phil. Soc. v.99 Lindel$\"{o}$f locales and realcompactness Madden, J.;J. Vermeer
  11. Cat. Alg. and Top. Realcompact-fine Alexandroff spaces A. Gilmour, C.R.A.
  12. General Lattice Theory Gr$\"{a}$tzer, G.
  13. Lect. Notes in Math. v.871 The duality of distributive-continuous lattices Banaschewski, B.
  14. Houston J. Math. v.4 Hulls, kernels, and continuous lattices Banaschewski, B.
  15. Kyungpook Math. J. v.39 Filters and Strict Extensions of Frames Banaschewski, B.;S.S. Hong
  16. Studies in Logic and the foundations of Mathematics Heyting, G.
  17. Proc. Cambridge Philos. v.67 On topological quotient maps preserved by pull-backs or products Day, B.J.;G.M. Kelly
  18. Trans. Amer. Math. Soc. v.40 The theory of representations for Boolean algebras Stone, M.H.
  19. J. of KMS v.25 On Countably Approximating Lattices Lee, S.O.
  20. Proc. Camb. Phil. Soc. v.29 On the combination of subalgebras Birkhoff G.
  21. 한국수학사학회지 v.12 no.1 직관주의 논리 이승온
  22. Semigroup Forum 8 Continuous posets and adjoint sequences Hoffmann, R.-E.
  23. Lattice Theory(3rd ed.) Birkhoff, G.
  24. 한국수학사학회지 v.12 no.2 격자론의 기원 홍영희
  25. S$\'{e}$minaire Ehresmann(Topologie et G$\'{e}$om$\'{e}$trie Diff$\'{e}$rentielle)(1re ann$\'{e}$e) no.2 Treillis locaux et paratopologies B$\'{e}$nabou, J.