Geodesic
A Genuine Topology for the Field of Mikusiński Operators
Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 297-299

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Struble, Raimond A. A Genuine Topology for the Field of Mikusiński Operators. Canadian mathematical bulletin, Tome 11 (1968) no. 2, pp. 297-299. doi: 10.4153/CMB-1968-038-8
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[1] 1. Mikusiński, J. G., Operational calculus. (Pergamon Press, London and New York, 1959). Google Scholar

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

[3] 3. Boehern, T. K., On sequences of continuous functions and convolutions. Studia Math. 25 (1965) 333-335. Google Scholar

[4] 4. Kisyński, J., Convergence du type L. Colloq. Math. 7 (1956–60) 205-211. Google Scholar

[5] 5. Dudley, R.M., On sequential convergence. Trans. Am. Math. Soc. 112 (1964) 483-507. Google Scholar

[6] 6. Erdelyi, A., Operational calculus and generalized functions. (Holt, Rinehart and Winston, New York, 1962). Google Scholar

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