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Weakly Pseudocompact Frames

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Abstract

We define the notion of weak pseudocompactness for frames and present several characterizations. Among them are characterizations in terms of strong inclusions, uniformities and cozero bases. Noteworthy is the fact that these internal characterizations are not translated from characterizations of weakly pseudocompact spaces.

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References

  1. Ball, R.N., Walters-Wayland, J.: C- and C *-quotients in pointfree topology. Dissertationes Mathematicae (Rozprawy Mat.), vol. 412 (2002)

  2. Ball, R.N., Walters-Wayland, J.: Well-embedding and G δ -density in a pointfree setting. Appl. Categ. Structures 14, 351–355 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Banaschewski, B.: Compactification of frames. Math. Nachr. 148, 59–69 (1990)

    MathSciNet  Google Scholar 

  4. Banaschewski, B.: Completion in pointfree topology. Lecture Notes in Math. and Appl. Math. No. 2/96, Univ. Cape town, (1996)

  5. Banaschewski, B., Gilmour, C.: Pseudocompactness and the cozero part of a frame. Comment. Math. Univ. Carolin. 37(3), 577–587 (1996)

    MATH  MathSciNet  Google Scholar 

  6. Banaschewski, B., Gilmour, C.: Cozero bases of frames. J. Pure Appl. Algebra 157, 1–22 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Banaschewski, B., Gilmour, C.: Realcompactness and the cozero part of a frame. Appl. Categ. Structures 9, 395–417 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Banaschewski, B., Mulvey, C.J.: Stone–Čech compactifications of locales I. Houston J. Math. 6(3), 301–312 (1980)

    MATH  MathSciNet  Google Scholar 

  9. Dube, T.: A little more on coz-unique frames. (submitted)

  10. Dube, T., Matutu, P.: A few points on pointfree pseudocompactness. Quaestiones Math. 30(4), 451–464 (2007)

    MATH  MathSciNet  Google Scholar 

  11. Dube, T., Walters-Wayland, J.: Coz-onto frame maps and some applications. Appl. Categ. Structures 15, 119–133 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Eckertson, F.W.: Sums, products, and mappings of weakly pseudocompact spaces. Topology Appl. 72, 149–157 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Eckertson, F.W., Ohta, H.: Weak pseudocompactness and zero sets in pseudocompact spaces. Houston J. Math. 22, 737–748 (1996)

    MATH  MathSciNet  Google Scholar 

  14. Garcia-Ferreira, S., Garcia-Maynez, A.: On weakly-pseudocompact spaces. Houston J. Math. 20, 145–159 (1994)

    MATH  MathSciNet  Google Scholar 

  15. Johnstone, P.T.: Stone Spaces. Cambridge Univ. Press, Cambridge (1982)

    MATH  Google Scholar 

  16. Marcus, N.: Realcompactifications of frames, Masters Dissertation. University of Cape Town (1994)

  17. Naidoo, I.: A note on precompact uniform frames. Topology Appl. 153, 941–947 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pultr, A.: Frames, In: Hazewinkel, M. (ed.) Handbook of Algebra, vol. 3, pp. 791–857. Elsevier Science B.V. (2003)

  19. Walters, J.L.: Uniform sigma frames and the cozero part of uniform frames. Masters Dissertation, University of Cape town (1990)

  20. Walters-Wayland, J.L.: Completeness and nearly fine uniform frames. Doctoral Thesis, University Catholique de Louvain (1995)

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003, Unisa, South Africa

    Themba Dube

  2. Department of Mathematics, University of Denver, Denver, CO, 80208, USA

    Joanne Walters-Wayland

Authors
  1. Themba Dube
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  2. Joanne Walters-Wayland
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Correspondence to Themba Dube.

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Dube, T., Walters-Wayland, J. Weakly Pseudocompact Frames. Appl Categor Struct 16, 749–761 (2008). https://doi.org/10.1007/s10485-007-9115-2

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  • DOI: https://doi.org/10.1007/s10485-007-9115-2

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