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Russia Yekaterinburg
Year
2012
Issue
1
Pages
41-49
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Section Mathematics
Title The dual of $C_{rc}(X)$
Author(-s) Osipov A.V.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
Abstract This is a study of the dual space of continuous linear functionals on the function space $C_{rc}(X)$. Here $rc$ denotes the $C$-compact-open topology on $C(X)$, the set of all real-valued continuous functions on a Tychonoff space $X$. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. The separability of this dual space has been studied.
Keywords сontinuous linear functional, function space, C-compact subset, C-compact-open topology, measure, zero set, separability
UDC 517.982.272, 515.122.55
MSC 54C40, 54C35, 54D60
DOI 10.20537/vm120105
Received 14 January 2012
Language Russian
Citation Osipov A.V. The dual of $C_{rc}(X)$, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 1, pp. 41-49.
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