Summary
This paper studies from the viewpoint of vector fibrations and vector spaces of cross-sections, endowed with appropriate topologies, the realm of ideas and results centered around the Weierstrass-Stone Theorem for algebras and modules of continuous functions in the real and self-adjoint complex cases. The proof of the equivalence between the separating and the general cases of such results by means of a quotient construction motivates the use of vector fibrations.
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Sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462 and by the National Science Foundation under NSF grant: GP 22713.
Introduced by G. Sansone.
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Machado, S., Prolla, J.B. An introduction to Nachbin spaces. Rend. Circ. Mat. Palermo 21, 119–139 (1972). https://doi.org/10.1007/BF02844237
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DOI: https://doi.org/10.1007/BF02844237