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Order-bounded convergence structures on spaces of continuous functions

Published online by Cambridge University Press:  09 April 2009

M. Schroder
M. Schroder
Affiliation:
Department of Mathematics University of Waikato, New Zealand
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Abstract

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This paper deals with solid topologies and convergence structures on the vector-lattice CX (the set of all continuous real-valued functions on a space X): the closed ideals and locally convex topologies associated with such structures are studied in particular. The work stems from E. Hewitt's paper on bounded linear functionals, touches on the classical theorems of L. Nachbin, T. Shirota and others (determining when the topology of compact convergence is barrelled or bornological), and extends some recent results on the duality between x and CX.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 35; secondary 54 A 20.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 39 - 61
Copyright
Copyright © Australian Mathematical Society 1979

References

Binz, E. (1975), Continuous convergence on C(X) (Lecture note in mathematics 469, Springer-Verlag, Berlin).CrossRefGoogle Scholar
Feldman, W. A. (1974), ‘A characterization of the topology of compact convergence on C(x)’, Pacific J. Math. 51, 109–119.CrossRefGoogle Scholar
Fischer, H. R. (1959), ‘Limesräume’, Math. Ann. 137, 269–303.CrossRefGoogle Scholar
Gillman, L. and Jerison, M. (1960), Rings of continuous functions (van Nostrand, New York).Google Scholar
Gulick, F. and Gulick, D. (1976), ‘Boundedness for spaces of continuous functions’, Rocky Mountain J. Math. 6, 247–263.Google Scholar
Hewitt, E. (1950), ‘Linear functionals on spaces of continuous functions’, Fund. Math. 37, 161–189.CrossRefGoogle Scholar
Kowalsky, H.-J. (1954), ‘Limesräume und Komplettierung’, Math. Nachr. 12, 301–340.Google Scholar
Kutzler, K. (1974), ‘UÜber einige Limitierungen auf C(X) und den Satz von Dini’, Math. Nachr. 64, 149–170.CrossRefGoogle Scholar
Nachbin, L. (1954), ‘Topological vector spaces of continuous functions’, Proc. Nat. Acad. Sci. 40, 471–474.CrossRefGoogle ScholarPubMed
Nanzetta, P. and Plank, D. (1972), ‘Closed ideals in C(X)’, Proc. Amer. Math. Soc. 35, 601–606.Google Scholar
Peressini, A. L. (1967), Ordered topological vector spaces (Harper and Row, New York).Google Scholar
Schroder, M. (1973), ‘Solid convergence spaces’, Bull. Austral. Math. Soc. 8, 443–459.CrossRefGoogle Scholar
Schroder, M. (1974), ‘A family of c-embedded spaces whose associated completely regular topology is compact’, Arch. Math. 25, 69–74.CrossRefGoogle Scholar
Schroder, M. (1976), ‘Marinescu structures and c-spaces’, Proceedings of the special session on convergence structures, pp. 204–235 (University of Nevada, Reno, Nevada).Google Scholar
Wloka, J. (1963), ‘Limesräume und Distributionen’, Math. Ann. 152, 351–409.CrossRefGoogle Scholar