Kyungpook Mathematical Journal

  • 제45권4호
  • /
  • Pages.455-470
  • /
  • 2005
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

Variants of Compactness in Pointfree Topology

  • Banaschewski, Bernhard (Department of Mathematics and Statistics, McMaster University) ;
  • Hong, Sung Sa (Department of Mathematics, Sogang University)
  • 투고 : 2005.09.06
  • 발행 : 2005.12.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

키워드

참고문헌

  1. Lecture Notes in Mathematics & Applied Mathematics no.2/96 Completion in pointfree topology Banaschewski, B.
  2. Quaest. Math. v.22 Propositional logic, frames, and fuzzy logic Banaschewski, B.
  3. Appl. Categorical Structures v.9 The axiom of countable choice and pointfree topology Banaschewski, B.
  4. Cahiers top. geom. diff. categ. Projective Frames : A General View Banaschewski, B.
  5. Kyungpook Math. J. v.39 Filters and strict extensions of frames Banaschewski, B.;Hong, S.S.
  6. Appl. Categorical Structures v.8 Extension by continuity in pointfree topology Banaschewski, B.;Hong, S.S.
  7. Kyungpook Math. J. v.42 General filters and strict extensions in pointfree topology Banaschewski, B.;Hong, S.S.
  8. Quaest. Math. v.19 On the completion of nearness frames Banaschewski, B.;Hong, S.S.;Pultr, A.
  9. Math. Proc. Cambridge Phil. Soc. v.108 Samuel compactification and completion of uniform frames Banaschewski, B.;Pultr, A.
  10. Colloq. Math. Soc. Janos Bolyai v.8 Separation axioms for frames Dowker, C.H.;Papert Strauss, D.
  11. London Math. Soc. Lecture Notes Series v.93 $T_1$ and $T_2$ axioms for frames Dowker, C.H.;Strauss, D.
  12. Kyungpook Math. J. v.35 Convergence in frames Hong, S.S.
  13. Appl. Categorical Structtures v.3 Cauchy completions of nearness frames Hong, S.S.;Kim, Y.K.
  14. Math. Scand. v.31 Atomless parts of spaces Isbell, J.R.
  15. Stone spaces, Cambridge Studies in Advanced Mathematics 3 Johnstone, P.T.
  16. Topology via Logic, Cambridge Tracts in Theor. Comp. Sci. No 5 Vickers, S.