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A Note on Certain Subalgebras of C()

Published online by Cambridge University Press:  20 November 2018

Anthony W. Hager  and
Donald G. Johnson
Anthony W. Hager
Affiliation:
The University oj Rochester, Rochester, New York
Donald G. Johnson
Affiliation:
The New Mexico State University, Las Cruces, New Mexico
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Let be a completely regular Hausdorff space and C() the algebra of continuous real-valued functions on . In attempts to characterize abstractly those algebras that are isomorphic to C() for some , one produces subalgebras of C() which: (a) contain the constant functions, (b) separate points and closed sets in , (c) are closed under uniform convergence, and (d) are closed under inversion in C() (see, for example, (2; 5)).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 389 - 393
Copyright
Copyright © Canadian Mathematical Society 1968

References

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