Abstract
We prove, for the class of real locally convex spacesE that are continuously and linearly injectable into somec0(Γ), that every non-zero homomorphism on the algebraC∞ (E) ofC∞-functions onE is given by a point evaluation at some point ofE. Furthermore, if every real-valuedC∞-function on the weak topology of a quasi-complete locally convex spaceE is bounded on a subsetA ofE, thenA is relatively weakly compact.
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