Geodesic
The dual of $C_{rc}(X)$
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 41-49
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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.
Keywords: сontinuous linear functional, function space, $C$-compact subset, $C$-compact-open topology, measure, zero set, separability. 
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A. V. Osipov. The dual of $C_{rc}(X)$. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2012), pp. 41-49. http://geodesic.mathdoc.fr/item/VUU_2012_1_a4/

[1] Aliprantis C. D., Burkinshaw O., Positive operators, Academic Press, Orlando, 1985 | MR | Zbl

[2] Arens R., Dugundji J., “Topologies for function spaces”, Pacific J. Math., 1951, no. 1, 5–31 | DOI | MR | Zbl

[3] Kundu S., “Spaces of continuous linear functionals: something old and something new”, Topology Proceedings, 14:1 (1989), 113–129 | MR | Zbl

[4] Kundu S., “The dual of $C_{ps}(X)$”, Positivity, 13 (2009), 367–384 | DOI | MR | Zbl

[5] Kundu S., Garg P., “Countability properties of the pseudocompact-open topology on $C(X)$”, Rend. Istit. Mat. Univ. Trieste, 39 (2007), 421–444 | MR | Zbl

[6] Osipov A. V., “The Set-Open topology”, Topology Proceedings, 37 (2011), 181–204 | MR

[7] Osipov A. V., “Topological-algebraic properties of function spaces with set-open topologies”, Topology and its Applications, 159:3 (2012), 800–805 | DOI | MR | Zbl

[8] Osipov A. V., “Svoistva $C$-kompaktno-otkrytoi topologii na prostranstve funktsii”, Trudy IMM UrO RAN, 17, no. 4, 2011, 258–277

[9] Osipov A. V., Kosolobov A. V., “O sekventsialno-kompaktno-otkrytoi topologii”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2011, no. 3, 75–84

[10] Fox R. H., “On topologies for function spaces”, Bull. Amer. Math. Soc., 51 (1945), 429–432 | DOI | MR | Zbl