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Uniformly locally connected uniform σ-frames

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Abstract

We introduce and study the concept of a uniformly locally connected uniform σ-frame. The uniformly locally connected reflection of a locally connected uniform σ-frame is constructed.

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References

  1. D. Baboolal, Local connectedness made uniform, Appl. Cat. Structures, 8 (2000), 377–390.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Baboolal and B. Banascheswki, Compactifications and local connectedness of frames, J. Pure and Appl. Algebra, 70 (1991), 3–16.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Banaschewski, The frame envelope of a σ-frame, Quaest. Math., 16 (1993), 51–60.

    MATH  MathSciNet  Google Scholar 

  4. B. Banaschewski, Completion in Pointfree Topology, Lecture Notes in Math, and Applied Math., Univ. of Cape Town, SoCat 94, No2/(1996).

  5. B. Banaschewski and C. Gilmour, Stone-Čech compactification and dimension theory for regular σ-frames, J. London Math. Soc., (2), 39 (1989), 1–8.

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  7. B. Banaschewski and A. Pultr, Samuel compactification and completion of uniform frames, Math. Proc. Camb. Phil. Soc., 108 (1990), 63–78.

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Banaschewski and A. Pultr, Paracompactness revisited, Appl. Cat. Structures, 1 (1993), 181–190.

    Article  MATH  MathSciNet  Google Scholar 

  9. B. Banaschewski and A. Pultr, Cauchy points of uniform and nearness frames, Quaest. Math., 19 (1996), 101–127.

    MATH  MathSciNet  Google Scholar 

  10. Gleason, Universal locally connected refinements, Illinois J. Math., 7 (1963), 521–531.

    MATH  MathSciNet  Google Scholar 

  11. I. Naidoo, Samuel compactification and uniform corefiection of nearness σ-frames, Czech. Math. J., 56(131) (2006), 1229–1241.

    Article  MATH  MathSciNet  Google Scholar 

  12. I. Naidoo, Connectedness extended to σ-frames, Acta Math. Hungar., accepted (2007).

  13. P. T. Johnstone, Stone Spaces, Cambridge Studies in Advanced Math. No. 3, Camb. Univ. Press (1982).

  14. J. L. Walters, Uniform sigma frames and the cozero part of uniform frames, Masters Dissertation, Univ. of Cape Town (1990).

  15. J. L. Walters, Compactifications and uniformities on σ-frames, Comm. Math. Univ. Carolinae, 32 (1991), 189–198.

    MATH  MathSciNet  Google Scholar 

  16. J. L. Walters-Wayland, Completeness and nearly fine uniform frames, PhD Thesis, Univ. Catholique de Louvain (1996).

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Authors and Affiliations

  1. School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, 2050, Gauteng, South Africa

    I. Naidoo

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  1. I. Naidoo
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Correspondence to I. Naidoo.

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Naidoo, I. Uniformly locally connected uniform σ-frames. Acta Math Hung 122, 373–385 (2009). https://doi.org/10.1007/s10474-008-8046-1

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  • DOI: https://doi.org/10.1007/s10474-008-8046-1

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