On the Stone-Weierstrass theorem for the strict and superstrict topologies

Author:
R. G. Haydon

Journal:
Proc. Amer. Math. Soc. **59** (1976), 273-278

MSC:
Primary 46E10

MathSciNet review:
0420236

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Abstract: Sentilles has introduced topologies and on the space of all bounded, continuous, real-valued functions on the completely regular space , which yield as dual spaces the three important spaces of measures, and , respectively. A number of authors have proved a Stone-Weierstrass theorem for , the coarsest of the three topologies. In this paper, it is shown that the superstrict topology does not obey the Stone-Weierstrass theorem, except perhaps when . Examples are then given to show that the situation for itself is rather complicated.

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DOI:
https://doi.org/10.1090/S0002-9939-1976-0420236-X

Article copyright:
© Copyright 1976
American Mathematical Society