Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
권호 표지

Continuous Flames and Countably Approximating Frames

  • Published : 2000.12.01
Download PDF
⟨ Previous Next ⟩

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. Houston J. Math. v.4 Hulls, kernels, and continuous lattices Banaschewski, B.
  2. Lect. Notes in Math. v.871 Coherent frames Banaschewski, B.
  3. Lect. Notes in Math. v.871 The duality of distributive-continuous lattices Banaschewski, B.
  4. Kyungpook Math. J. v.39 Filters and Strict Extensions of Frames Banaschewski, B.;S.S. Hong
  5. 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.
  6. Proc. Camb. Phil. Soc. v.29 On the combination of subalgebras Birkhoff G.
  7. Lattice Theory(3rd ed.) Birkhoff, G.
  8. Proc. Cambridge Philos. v.67 On topological quotient maps preserved by pull-backs or products Day, B.J.;G.M. Kelly
  9. Festschrift Techn. Hoch. Braunschweig;Ges. Werke v.Ⅱ $\"{U}$ber Zerlegungen von Zahlen durch ihre gr$\"{o}$ssten gemeinsamen Teiler Dedekind, R.
  10. A Compendium of Continuous Lattices Gierz, G.;K.H. Hofmann;K. Keimel;J.D. Lawson;M. Mislove;D.S. Scott
  11. Cat. Alg. and Top. Realcompact-fine Alexandroff spaces A. Gilmour, C.R.A.
  12. General Lattice Theory Gr$\"{a}$tzer, G.
  13. Universal Algebra Gr$\"{a}$tzer, G.
  14. Studies in Logic and the foundations of Mathematics Heyting, G.
  15. Semigroup Forum 8 Continuous posets and adjoint sequences Hoffmann, R.-E.
  16. Lect. Notes in Math. v.871 Continuous posets, prime spectra of completely distributive complete lattices, and Hausdorff compactifications Hoffmann, R.-E.
  17. Stone Space Johnstone, P.T.
  18. J. London Math. Soc. v.2 Topological semilattices with small semilattices Lawson, J.D.
  19. J. of KMS v.25 On Countably Approximating Lattices Lee, S.O.
  20. Math. Proc. Cambridge Phil. Soc. v.99 Lindel$\"{o}$f locales and realcompactness Madden, J.;J. Vermeer
  21. Lect. Notes in Math. v.274 Continuous lattices Scott, D.S.
  22. Trans. Amer. Math. Soc. v.40 The theory of representations for Boolean algebras Stone, M.H.
  23. Ann. Math. v.3a Lattices and topological spaces Wallman, H.
  24. 한국수학사학회지 v.12 no.1 직관주의 논리 이승온
  25. 한국수학사학회지 v.12 no.2 격자론의 기원 홍영희