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Regular completions of Cauchy spaces via function algebras

Published online by Cambridge University Press:  17 April 2009

R.J. Gazik  and
D.C. Kent
R.J. Gazik
Affiliation:
Department of Mathematics, Arkansas State University, State University, Arkansas, USA
D.C. Kent
Affiliation:
Department of Pure and Applied Mathematics, Washington State University, Pullman, Washington, USA.
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Abstract

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A regular completion with the universal property is obtained for each member of a certain class of Cauchy spaces by embedding the Cauchy space in a complete function algebra with the continuous convergence structure.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 1 , August 1974 , pp. 77 - 88
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Binz, E., “Bemerkungen zu limitierten Funktionenalgebren”, Math. Ann. 175 (1968), 169–184.CrossRefGoogle Scholar
[2]Binz, E., “Zu den Beziehungen zwischen c–einbettbaren Limesräumen und ihren limitierten Funktionenalgebren”, Math. Ann. 181 (1969), 45–52.CrossRefGoogle Scholar
[3]Cook, C.H. and Fischer, H.R., “Uniform convergence structures”, Math. Ann. 173 (1967), 290–306.CrossRefGoogle Scholar
[4]Feldman, William A., “Axioms of countability and the algebra C(X)”, Pacific J. Math. 47 (1973), 81–89.CrossRefGoogle Scholar
[5]Keller, H.H., “Die Limes-Uniformisierbarkeit der Limesräume”, Math. Ann. 176 (1968), 334–341.CrossRefGoogle Scholar
[6]Kent, D.C. and Richardson, G.D., “Regular completion of Cauchy spaces”, Pacific J. Math. (to appear).Google Scholar
[7]McKennon, Kelly, “The strict topology and the Cauchy structure of the spectrum of a C*-algebra”, submitted.Google Scholar
[8]Ramaley, J.F. and Wyler, Oswald, “Cauchy spaces. I. Structure and uniformization theorems”, Math. Ann. 187 (1970), 175–186.CrossRefGoogle Scholar
[9]Ramaley, J.F. and Wyler, Oswald, “Cauchy spaces. II. Regular completions and compactifications”, Math. Ann. 187 (1970), 187–199.CrossRefGoogle Scholar
[10]Reed, Ellen E., “Completions of uniform convergence spaces”, Math. Ann. 194 (1971), 83–108.CrossRefGoogle Scholar
[11]Schroder, M., “Solid convergence spaces”, Bull. Austral. Math. Soc. 8 (1973), 443–459.CrossRefGoogle Scholar
[12]Schroder, M., Richardson, G., McKennon, K., Kent, D., “Continuous convergence in C(X)”, Pacific J. Math. (to appear).Google Scholar