Journal for History of Mathematics (한국수학사학회지)

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

Stably 가산 근사 Frames와 Strongly Lindelof Frames

  • Published : 2003.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper is a sequel to [11]. We introduce $\sigma$-coherent frames, stably countably approximating frames and strongly Lindelof frames, and show that a stably countably approximating frame is a strongly Lindelof frame. We also show that a complete chain in a Lindelof frame if and only if it is a strongly Lindelof frame by using the concept of strong convergence of filters. Finally, using the concepts of super compact frames and filter compact frames, we introduce an example of a strongly Lindelof frame which is not a stably countably approximating frame.

Keywords

References

  1. Kyungpook Math J. v.39 Filters and strict extensions of frames B. Banaschewski;S. S. Hong
  2. preprint Variants of compactness in pointfree topology B. Banaschewski;S. S. Hong
  3. Appl. Categ. Structures v.9 Adjointness aspects of the down-set functor B. Banaschewshi;A. Pultr
  4. A Compendium of Continuous Lattices G. Gierz;K. H. Hofmann;K. Keimel;J. D. Lawsonm;M. Mislove;D. S. Scott;
  5. Math. Proc. Cambridge Phil. Soc. v.96 Realcompact spaces and regular σ-frames C.R.A. Gilmour
  6. Stone Space P. T. Johnstone
  7. J. of KMS v.25 On Countably Approximating Lattices S. O. Lee
  8. Comm. Korean Math. Coc. v.17 no.2 Countably Apoproximating Frames S. O. Lee
  9. Math. Proc. Cambridge Phil. Soc. v.99 Lindelof locales and realcompactness J. Madden;J. Vermeer
  10. Lect. Notes in Math v.274 Continuous Lattices D. S. Scott
  11. Continuous Frames and Countably Approximating Frames v.13 no.2 이승온