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Characters on algebras of smooth functions

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Abstract

For a huge class of spaces it is shown that the real characters on the algebra of differentiable functions are exactly the evaluations at points.

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References

  1. R. Bonic, J. Frampton: Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966), 877–898.

    Google Scholar 

  2. R. Engelking: Outline of general topology, North Holland 1968.

  3. A. Frölicher: Smooth structures, in: Springer Lecture Notes 962 (1982), 69–81.

    Google Scholar 

  4. A. Frölicher, B. Gisin, A. Kriegl: General differentiation theory, in: Category theoretic methods in geometry Proc., Aarhus (1983), p. 125–153.

  5. A. Frölicher, B. Griegl: Linear spaces and Differentiation Theory, John Wiley & Sons, Chichester 1988.

    Google Scholar 

  6. L. Gilman, M. Jerison: Rings of continuous functions, van Nostrand 1960.

  7. H. H. Keller: Differential calculus in locally convex spaces. Springer Lecture Notes 417, 1974.

  8. A. Kock: Synthetic differential geometry, London Math. Soc. Lect. Notes Series 51, 1981.

  9. A. Kriegl: Die richtigen Räume für Analysis im Unendlich-Dimensionalen, Monatshefte f. Math. 94 (1982), 109–124.

    Google Scholar 

  10. A. Kriegl: Eine kartesisch abgeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektorräumen, Monatshefte f. Math. 95 (1983), 287–309.

    Google Scholar 

  11. A. Kriegl: A cartesian closed extension of the category of Banach manifolds, in: Categorical Topology, Proc. Conference Toledo, Ohio, 1983, (1984), p. 323–336.

  12. E. B. Leach, J. H. M. Whitfield: Differentiable functions and rough norms on Banach spaces, Proc. AMS 33 (1972), 120–126.

    Google Scholar 

  13. S. Mazur: On continuous mappings on cartesian products, Fund. Math. 39 (1952), 229–238.

    Google Scholar 

  14. P. Michor: Manifolds of differentiable mappings, Shiva Math. Series 3. 1980 Orpington.

  15. P. Michor: Manifolds of smooth mappings IV, Cahiers Top. Geom. Diff. 24 (1983), 57–86.

    Google Scholar 

  16. P. Michor: A convenient setting for differential geometry and global analysis, Cahiers Top. Geom. Diff. 25 (1984), 63–112.

    Google Scholar 

  17. J. W. Milnor, J. D. Stashieff: Characteristics Classes, Ann. of Math. Stud., princeton Univ. Press, 1974 Princeton.

  18. I. Moerdijk, G. E. Reyes:C∝-Rings, preprint 1984 Montreal.

  19. R. Sikorski: Differential Modules, Colloq. M. 24 (1971), 45–79.

    Google Scholar 

  20. H Torunzcyk: Smooth partitions of unity on some non-separable Banach spaces. Stud. Math. 46 (1973), 43–51.

    Google Scholar 

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Kriegl, A., Michor, P. & Schachermayer, W. Characters on algebras of smooth functions. Ann Glob Anal Geom 7, 85–92 (1989). https://doi.org/10.1007/BF00127859

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