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The Stone-Weierstrass theorem for wallman rings

Part of: Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 April 2009

H. L. Bentley  and
B. J. Taylor
H. L. Bentley
Affiliation:
The University of ToledoToledo Ohio 43606, USA
B. J. Taylor
Affiliation:
IBM Corporation Sylvania Ohio 43560, USA
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Abstract

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Biles has called a subring A of the ring C(X) a Wallman ring on X whenever Z(A), the zero sets of function belonging to A, forms a normal base on X in the sense of Frink (1964). In the following, we are concerned with the uniform topology of C(X). We formulate and prove some generalizations of the Stone–Weierstrass theorem in this setting.

MSC classification

Secondary: 54C30: Real-valued functions 54C40: Algebraic properties of function spaces 54C50: Special sets defined by functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 230 - 240
Copyright
Copyright © Australian Mathematical Society 1978

References

REFERENCES

All references refer to those listed at the end of the immediately preceding paper: Bentley, H. L. and Taylor, B. J. (1978), “On generalizations of C*embedding for Wallman rings”, J. Austral. Math. Soc. 25 (Ser. A), 215–229.CrossRefGoogle Scholar