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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
2. Urbanik, K., Sur la structure non topologique du corps des opérateurs. Studia Math. 14 (1954) 243-246.Google Scholar
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