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u-Singularity and t-Topos Theoretic Entropy

Abstract

We will give descriptions of u-singularities as we introduce the notion of t-topos theoretic entropies. The unifying methodology for a u-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an object in t-site in the theory of temporal topos.

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References

  1. Butterfield, J., Isham, C.J.: Spacetime and the philosophical challenge of quantum gravity, arxiv:gr-qc/9903072 v1, 18 Mar 1999

  2. Butterfield, J., Isham, C.J.: Int. J. Theor. Phys. 38, 2669 (1998). quant-ph/9803055

    MathSciNet  Google Scholar 

  3. Butterfield, J., Isham, C.J.: Int. J. Theor. Phys. 37, 827 (1999). quant-ph/9808067

    Article  MathSciNet  Google Scholar 

  4. Mallios, A., Raptis, I.: Finitary, causal and quantal vacuum Einstein gravity. Int. J. Theor. Phys. 42, 1479 (2003). gr-qc/0209048

    Article  MATH  MathSciNet  Google Scholar 

  5. Raptis, I.: Finitary-algebraic ‘resolution’ of the inner Schwarzschild singularity. Int. J. Theor. Phys. (2004). gr-qc/0408045

  6. Penrose, R.: The Road to Reality. Alfred A. Knopf, New York (2005)

    MATH  Google Scholar 

  7. Grauert, H., Remmert, R.: Coherent Analytic Sheaves, Grundlehren der Mathematischen Wissenschaften, vol. 265. Springer, Berlin (1984)

    MATH  Google Scholar 

  8. Kato, G., Struppa, D.C.: Fundamentals of Algebraic Microlocal Analysis, Pure and Applied Math., vol. 217, Marcel Dekker Inc., New York (1999)

    MATH  Google Scholar 

  9. Kato, G.: The Heart of Cohomology. Springer, Berlin (2006)

    MATH  Google Scholar 

  10. Kato, G.: Elemental principles of t-topos. Europhys. Lett. 68(4), 467–472 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  11. Kato, G.: Elemental t.g. principles of relativistic t-topos. Europhys. Lett. 71(2), 172–178 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  12. Gelfand, S.I., Manin, Y.I.: Methods of Homological Algebra. Springer, Berlin (1996)

    MATH  Google Scholar 

  13. Kashiwara, H., Schapira, P.: Sheaves and Categories. Springer, Berlin (2006)

    MATH  Google Scholar 

  14. Kato, G., Tanaka, T.: Double-slit interference and temporal topos. Found. Phys. 36(11), 1681–1700 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. Kato, G., Kafatos, M., Roy, S., Tanaka, T.: Sheaf theory and geometric approach to EPR nonlocality (submitted)

  16. Kato, G.: Mathematical foundations for the theory of t-topos (in preparation)

  17. Kato, G., Takemae, S.A.: Hawking radiation and t-topos (in preparation)

  18. Genovese, M.: Research on hidden variable theories: A review of recent progresses. Phys. Rep. 413, 319–396 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  19. Vladimirov, V.S., Volovich, I.V., Zelenov, E.I.: p-Adic Analysis and Mathematical Physics. World Scientific, Singapore (1994)

    Google Scholar 

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Correspondence to Goro C. Kato.

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Kato, G.C. u-Singularity and t-Topos Theoretic Entropy. Int J Theor Phys 49, 1952–1960 (2010). https://doi.org/10.1007/s10773-010-0380-8

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  • DOI: https://doi.org/10.1007/s10773-010-0380-8

Keywords

  • Light Cone
  • Direct Limit
  • Inverse Limit
  • Virtual Topology
  • Sheaf Theory