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A Characterization of the Algebra of Functions Vanishing at Infinity

Published online by Cambridge University Press:  20 November 2018

Robert E. Mullins
Robert E. Mullins*
Affiliation:
Marquette University, Milwaukee, Wisconsin
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1. In this paper, X will always denote a locally compact Hausdorff space, C0(X) the algebra of all complex-valued continuous functions vanishing at infinity on X and B(X) the algebra of all bounded continuous complex-valued functions defined on X. If X is compact, C0(X) is identical to B (X) and all the results of this paper are obvious. Therefore, we will assume at the outset that X is not compact. If A represents an algebra of functions, AR will denote the algebra of all real-valued functions in A.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 751 - 754
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Kelley, J. L., General topology (Van Nostrand, New York, 1955).Google Scholar
2. Mullins, R. E., Some results on algebras of functions, Ph.D. Thesis, Northwestern University, Evanston, Illinois, 1965.Google Scholar