You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Stone-Weierstrass Theorem for the Strict and Superstrict Topologies
R. G. Haydon
Proceedings of the American Mathematical Society
Vol. 59, No. 2 (Sep., 1976), pp. 273-278
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2041483
Page Count: 6
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
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.
Proceedings of the American Mathematical Society © 1976 American Mathematical Society