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## Archive of Issues

Russia Yekaterinburg
Year
2012
Issue
1
Pages
41-49
 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. References Aliprantis C.D., Burkinshaw O. Positive operators, Academic Press, Orlando, 1985. Arens R., Dugundji J. Topologies for function spaces, Pacific J. Math, 1951, no. 1, pp. 5–31. Kundu S. Spaces of continuous linear functionals: something old and something new, Topology Proceedings, 1989, no. 14 (1), pp. 113–129. Kundu S. The dual of $C_{ps}(X)$, Positivity, 2009, no. 13, pp. 367–384. Kundu S., Garg P. Countability properties of the pseudocompact-open topology on $C(X)$, Rend. Istit. Mat. Univ. Trieste, 2007, vol. XXXIX, pp. 421–444. Osipov A.V. The Set-Open topology, Topology Proceedings, 2011, no. 37, pp. 181–204. Osipov A.V. Topological-algebraic properties of function spaces with set-open topologies, Topology and its Applications, 2012, vol. 159, issue 3, pp. 800–805. Osipov A.V. Properties of the $C$-compact-open topology on a function space, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2011, vol. 17, no. 4, pp. 258–277. Osipov A.V., Kosolobov D.A. On sequentially compact-open topology, Vestn. Udmurt. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 3, pp. 75–84. Fox R.H. On topologies for function spaces, Bull. Amer. Math. Soc., 1945, no. 51, pp. 429–432. Full text