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Extending strongly continuous functions between apartness spaces

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Abstract

A natural extension theorem for strongly continuous mappings, the morphisms in the category of apartness spaces, is proved constructively.

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References

  1. Bishop, E.: Foundations of constructive analysis. McGraw–Hill New York 1967

  2. Bishop, E., Bridges, D.: Constructive analysis. Grundlehren der Math. Wissenschaften 279, Springer Verlag Heidelberg Berlin New York 1985

  3. Bourbaki, N.: General topology (Part 1). Addison–Wesley Reading MA 1966

  4. Bridges, D., Richman, F.: Varieties of Constructive Mathematics. London Math. Soc. Lecture Notes 97, Cambridge Univ. Press 1987

  5. Bridges, D., Vîţă, L.: Characterising near continuity constructively. Math. Logic Quarterly 47 (4), 535–538 (2001)

    Article  Google Scholar 

  6. Bridges, D., Vîţă, L.: Cauchy nets in the constructive theory of apartness spaces. Scientiae Math. Japonicae 56 (1), 123–132 (2002)

    MathSciNet  Google Scholar 

  7. Bridges, D., Vîţă, L.: Apartness spaces as a foundation for constructive topology. Ann. Pure Appl. Logic, 119, 61–83 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bridges, D., Vîţă, L.: Separatedness in Constructive Topology. Documenta Math. 8, 567–576 (2003)

    MATH  MathSciNet  Google Scholar 

  9. Bridges, D., Schuster, P., Vîţă, L.: Apartness, topology, and uniformity: a constructive view. In: Computability and Complexity in Analysis, (Proc. Dagstuhl Seminar 01461, 11–16 November 2001), Math. Log. Quart. 48, Suppl. 1, 16–28 (2002).

    Google Scholar 

  10. Cameron, P., Hocking, J.G., Naimpally, S.A.: Nearness—a better approach to topological continuity and limits. Mathematics Report #18–73, Lakehead University Canada 1973

  11. Diaconescu, R.: Axiom of choice and complementation. Proc. AMS 51, 176–178 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  12. Goodman, N., Myhill, J.: Choice implies excluded middle. Z. Math. Logik Grundlagen Math. 23, 461 (1978)

    Google Scholar 

  13. Herrlich, H.: On the extendibility of continuous functions. Gen Topology Appl. 5, 213–215 (1974)

    Article  MathSciNet  Google Scholar 

  14. Herrlich, H.: A concept of nearness. Gen. Topology Appl. 4, 191–212 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  15. Naimpally, S.A., Warrack, B.D.: Proximity Spaces. Cambridge Tracts in Math. and Math. Phys. 59, Cambridge at the University Press 1970

  16. Schuster, P., Vîţă, L., Bridges, D.: Apartness as a relation between subsets. In: Combinatorics, Computability and Logic. (Proceedings of DMTCS'01, Constanţa, Romania, 2–6 July 2001 C.S. Calude, M.J. Dinneen, S. Sburlan (eds), DMTCS Series 17, Springer Verlag London 203–214 (2001)

  17. Troelstra, A.S., van Dalen, D.: Constructivism in Mathematics: an introduction (two volumes). North Holland Amsterdam 1988

  18. Vîţă, L.: Proximal and uniform convergence on apartness spaces. Math. Logic Quarterly, 49 (3), 255–259 (2003)

    Article  Google Scholar 

  19. Vîţă, L., Bridges, D.: A constructive theory of point–set nearness. In: Proceedings of Topology in Computer Science: Constructivity; Asymmetry and Partiality; Digitization. Seminar in Dagstuhl, Germany, 4–9 June 2000; Springer Lecture Notes in Computer Science, 305, 473–489 (2003)

  20. Vîţă, L., Bridges, D.: More on cauchy nets in apartness spaces. Scientiae Math. Japonicae 9, 375–380 (2003)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Canterbury, Private Bag, 4800, Christchurch, New Zealand

    Luminiţa Simona Vîţă

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  1. Luminiţa Simona Vîţă
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Additional information

The author thanks Douglas Bridges and the anonymous referee for their useful suggestions, and the FoRST New Zealand for supporting her as a Postdoctoral Research Fellow (contract number UOCX0215) during the writing of this paper.

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Vîţă, L. Extending strongly continuous functions between apartness spaces. Arch. Math. Logic 45, 351–356 (2006). https://doi.org/10.1007/s00153-005-0299-6

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  • DOI: https://doi.org/10.1007/s00153-005-0299-6

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