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On generalizations of C*-embedding 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 (1970) has called a subring A of the ring C(X), of all real valued continuous functions on a topological space X, a Wallman ring on X whenever Z(A), the zero sets of functions belonging to A, forms a normal base on X in the sense of Frink (1964). Previously, we have related algebraic properties of a Wallman ring A to topological properties of the Wallman compactification w(Z(A)) of X determined by the normal base Z(A). Here we introduce two different generalizations of the concept of “a C*-embedded subset” and study relationships between these and topological (respectively, algebraic) properties of w(Z(A)) (respectively, A).

MSC classification

Secondary: 54C45: $C$- and $C^*$-embedding 54C40: Algebraic properties of function spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 2 , March 1978 , pp. 215 - 229
Copyright
Copyright © Australian Mathematical Society 1978

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