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A Genuine Topology for the Field of Mikusiński Operators

Published online by Cambridge University Press:  20 November 2018

Raimond A. Struble
Raimond A. Struble*
Affiliation:
North Carolina State University
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Let C denote the complex algebra of continuous functions of a non-negative real variable under addition, scalar multiplication and convolution. C has no divisors of zero and its quotient field F is called the field of Mikusiński operators [1]. It is well known that Mikusiński has defined a sequential convergence in F which is not topological [2]. Using a recent result due to T.K. Boehem [3] we shall provide F with a sequential convergence which is topological.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 2 , June 1968 , pp. 297 - 299
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Mikusiński, J. G., Operational calculus. (Pergamon Press, London and New York, 1959).Google Scholar
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3. Boehern, T. K., On sequences of continuous functions and convolutions. Studia Math. 25 (1965) 333-335.Google Scholar
4. Kisyński, J., Convergence du type L. Colloq. Math. 7 (1956–60) 205-211.Google Scholar
5. Dudley, R.M., On sequential convergence. Trans. Am. Math. Soc. 112 (1964) 483-507.Google Scholar
6. Erdelyi, A., Operational calculus and generalized functions. (Holt, Rinehart and Winston, New York, 1962).Google Scholar