Advertisement

From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory

  • Erik Palmgren
Part of the Synthese Library book series (SYLI, volume 341)

Keywords

Fundamental Group Homotopy Theory Constructive Mathematic Terminal Object Formal Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.A. Armstrong. Basic Topology. Springer, 1985.Google Scholar
  2. 2.
    B. Banaschewski, T. Coquand and G. Sambin (eds.). Papers presented at the Second Workshop Formal Topology, Venice, April 2–4, 2002. Special issue of Ann. Pure Appl. Logic 137, 2006.Google Scholar
  3. 3.
    B. Banaschewski and C.J. Mulvey. A constructive proof of the Stone-Weierstrass theorem. J. Pure Appl. Algebra 116, 25–40, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    M. Beeson. Foundations of Constructive Mathematics. Springer, 1985.Google Scholar
  5. 5.
    E. Bishop and D.S. Bridges. Constructive Analysis. Springer, 1985.Google Scholar
  6. 6.
    T. Coquand. An intuitionistic proof of Tychonoff’s theorem. J. Symbolic Logic 57, 28–32, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    L. Crosilla and P. Schuster (eds.). From Sets and Types to Topology and Analysis: Towards Practicable Foundations of Constructive Mathematics. Oxford Logic Guides, Oxford University Press, 2005.Google Scholar
  8. 8.
    G. Curi. Geometry of Observations: Some Contributions to (Constructive) Point-Free Topology. PhD Thesis, Siena, 2004.Google Scholar
  9. 9.
    H. Freudenthal. Zum intuitionistischen Raumbegriff. Compositio Math. 4, 82–111, 1936.zbMATHMathSciNetGoogle Scholar
  10. 10.
    H. Freudenthal and A. Heyting. The Life of L.E.J. Brouwer. In: H. Freudenthal (ed.), L.E.J. Brouwer, Collected Works, Vol. 2. North-Holland, 1976.Google Scholar
  11. 11.
    M.J. Greenberg. Lectures on Algebraic Topology. Benjamin, New York, 1967.zbMATHGoogle Scholar
  12. 12.
    W. He. Homotopy theory for locales. (Chinese). Acta Math. Sinica 46, (5), 951–960. (ISSN 0583-1431), 2003.zbMATHMathSciNetGoogle Scholar
  13. 13.
    P.T. Johnstone. Stone Spaces. Cambridge University Press, 1982.Google Scholar
  14. 14.
    P.T. Johnstone. The point of pointless topology. Bull. Amer. Math. Soc. 8, 41–53, 1983.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    A. Joyal and M. Tierney. An extension of the Galois theory of Grothendieck. Memoirs Amer. Math. Soc. 309, 1984.Google Scholar
  16. 16.
    J.F. Kennison. What is the fundamental group? J. Pure Appl. Algebra 59, 187–200, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    P. Martin-Löf. Notes on Constructive Mathematics. Almqvist and Wiksell, 1970.Google Scholar
  18. 18.
    E. Palmgren. Predicativity problems in point-free topology. In: V. Stoltenberg-Hansen and J. Vänänen (eds.), Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in Helsinki, Finland, August 14–20, 2003, Lecture Notes in Logic 24, AK Peters, 2006.Google Scholar
  19. 19.
    E. Palmgren. Continuity on the real line and in formal spaces. In: From Sets and Types to Topology and Analysis: Towards practicable Foundations of Constructive Mathematics. Oxford Logic Guides, Oxford University Press, 2005.Google Scholar
  20. 20.
    E. Palmgren. Regular universes and formal spaces, Ann. Pure Appl. Logic 137, 2006.Google Scholar
  21. 21.
    G. Sambin. Intuitionistic formal spaces — a first communication. In: D. Skordev (ed.), Mathematical Logic and its Applications. Plenum Press, pp. 187–204, 1987.Google Scholar
  22. 22.
    A.S. Troelstra. Intuitionistic General Topology. PhD Thesis, Amsterdam, 1966.Google Scholar
  23. 23.
    F. Waaldijk. Modern Intuitionistic Topology. PhD Thesis, Nijmegen, 1998.Google Scholar
  24. 24.
    M.E. Maietti. Predicative exponentiation of locally compact formal topologies over inductively generated ones. In: L. Crosilla and P. Schuster (eds.), From Sets and Types to Topology and Analysis: Towards Practicable Foundations of Constructive Mathematics, Oxford Logic Guides, Oxford University Press 2005.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Erik Palmgren
    • 1
  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

Personalised recommendations