Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sentilles has introduced topologies $ {\beta _0},\;\beta $ and $ {\beta _1}$ on the space $ {C_b}(S)$ of all bounded, continuous, real-valued functions on the completely regular space $ S$, which yield as dual spaces the three important spaces of measures, $ {M_t}(S),\;{M_\tau }(S)$ and $ {M_\sigma }(S)$, respectively. A number of authors have proved a Stone-Weierstrass theorem for $ {\beta _0}$, the coarsest of the three topologies. In this paper, it is shown that the superstrict topology $ {\beta _1}$ does not obey the Stone-Weierstrass theorem, except perhaps when $ {\beta _1} = \beta $. Examples are then given to show that the situation for $ \beta $ itself is rather complicated.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46E10

Retrieve articles in all journals with MSC: 46E10

Additional Information

Article copyright: © Copyright 1976 American Mathematical Society