Skip to main content
Log in

A Little More on Coz-Unique Frames

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

Coz-unique frames were defined and characterized by Banaschewski and Gilmour (J Pure Appl Algebra 157:1–22, 2001). In this note we give further characterizations of these frames along the lines of characterizations of absolutely z-embedded spaces obtained by Blair and Hager (Math Z 136:41–52, 1974) on the one hand, and by Hager and Johnson (Canad J Math 20:389–393, 1968) on the other. We also extend to frames certain characterizations of z-embedded spaces; namely, we give a characterization of coz-onto frame homomorphisms in terms of normal covers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alò, R.A., Imler, L., Shapiro, H.L.: P- and z-embedded subspaces. Math. Z. 188, 13–22 (1970)

    MATH  Google Scholar 

  2. Ball, R.N., Walters-Wayland, J.: C- and C *-quotients in pointfree topology. Dissertationes Mathematicae (Rozprawy Mat.), vol. 412, p. 62 (2002)

  3. Banaschewski, B., Brümmer, G.C.L.: Functorial uniformities on strongly zero-dimensional frames. Kyungpook Math. J. 41(2), 179–190 (2001)

    MATH  MathSciNet  Google Scholar 

  4. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Banaschewski, B., Pultr, A.: Paracompactness revisited. Appl. Categ. Structures 1, 181–190 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Blair, R.L.: A cardinal generalization of z-embedding. Rings of Continuous Functions (Cincinnati, Ohio, 1982), Lecture Notes in Pure and Appl. Math., vol. 95, pp. 7–66. Dekker, New York (1985)

    Google Scholar 

  9. Blair, R.L., Hager, A.W.: Extensions of zero-sets and of real-valued functions. Math. Z. 136, 41–52 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  10. Charalambous, M.G.: Direct constructions of the paracompact coreflections of frames. Appl. Categ. Structures 10(5), 521–530 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  12. Dube, T., Walters-Wayland, J.: Coz-onto frame maps and some applications. Appl. Categ. Structures 15(1–2), 119–133 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gillman, L., Jerison, M.: Rings of Continuous Functions. Van Nostrand, Princeton (1960)

    MATH  Google Scholar 

  14. Hager, A.W., Johnson, D.G.: A note on certain subalgebras of \(C(\mathfrak{X})\). Canad. J. Math. 20, 389–393 (1968)

    MATH  MathSciNet  Google Scholar 

  15. Hong, S.S.: Convergence in frames. Kyungpook Math. J. 35, 85–91 (1995)

    MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  17. Marcus, N.: Realcompactification of frames. Comment. Math. Univ. Carolin. 36(2), 347–356 (1995)

    MATH  MathSciNet  Google Scholar 

  18. Mrowka, S.: Functionals on uniformly closed rings of continuous functions. Fund. Math. 46, 81–87 (1958)

    MATH  MathSciNet  Google Scholar 

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

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Themba Dube.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dube, T. A Little More on Coz-Unique Frames. Appl Categor Struct 17, 63–73 (2009). https://doi.org/10.1007/s10485-008-9125-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10485-008-9125-8

Keywords

Mathematics Subject Classifications (2000)

Navigation