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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R. Bonic, J. Frampton: Smooth functions on Banach manifolds, J. Math. Mech. 15 (1966), 877–898.
R. Engelking: Outline of general topology, North Holland 1968.
A. Frölicher: Smooth structures, in: Springer Lecture Notes 962 (1982), 69–81.
A. Frölicher, B. Gisin, A. Kriegl: General differentiation theory, in: Category theoretic methods in geometry Proc., Aarhus (1983), p. 125–153.
A. Frölicher, B. Griegl: Linear spaces and Differentiation Theory, John Wiley & Sons, Chichester 1988.
L. Gilman, M. Jerison: Rings of continuous functions, van Nostrand 1960.
H. H. Keller: Differential calculus in locally convex spaces. Springer Lecture Notes 417, 1974.
A. Kock: Synthetic differential geometry, London Math. Soc. Lect. Notes Series 51, 1981.
A. Kriegl: Die richtigen Räume für Analysis im Unendlich-Dimensionalen, Monatshefte f. Math. 94 (1982), 109–124.
A. Kriegl: Eine kartesisch abgeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektorräumen, Monatshefte f. Math. 95 (1983), 287–309.
A. Kriegl: A cartesian closed extension of the category of Banach manifolds, in: Categorical Topology, Proc. Conference Toledo, Ohio, 1983, (1984), p. 323–336.
E. B. Leach, J. H. M. Whitfield: Differentiable functions and rough norms on Banach spaces, Proc. AMS 33 (1972), 120–126.
S. Mazur: On continuous mappings on cartesian products, Fund. Math. 39 (1952), 229–238.
P. Michor: Manifolds of differentiable mappings, Shiva Math. Series 3. 1980 Orpington.
P. Michor: Manifolds of smooth mappings IV, Cahiers Top. Geom. Diff. 24 (1983), 57–86.
P. Michor: A convenient setting for differential geometry and global analysis, Cahiers Top. Geom. Diff. 25 (1984), 63–112.
J. W. Milnor, J. D. Stashieff: Characteristics Classes, Ann. of Math. Stud., princeton Univ. Press, 1974 Princeton.
I. Moerdijk, G. E. Reyes:C∝-Rings, preprint 1984 Montreal.
R. Sikorski: Differential Modules, Colloq. M. 24 (1971), 45–79.
H Torunzcyk: Smooth partitions of unity on some non-separable Banach spaces. Stud. Math. 46 (1973), 43–51.
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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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DOI: https://doi.org/10.1007/BF00127859