Section
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Mathematics
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Title
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The dual of $C_{rc}(X)$
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Author(-s)
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Osipov A.V.a
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Affiliations
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Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
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Abstract
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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.
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Keywords
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сontinuous linear functional, function space, C-compact subset, C-compact-open topology, measure, zero set, separability
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UDC
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517.982.272, 515.122.55
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MSC
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54C40, 54C35, 54D60
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DOI
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10.20537/vm120105
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Received
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14 January 2012
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Language
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Russian
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Citation
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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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References
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- 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.
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