Separability and Sequential Separability of the Space <Emphasis Type="Italic">C</Emphasis>(<Emphasis Type="Italic">X</Emphasis>) |
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| Authors: | A V Osipov |
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| Institution: | 1.Krasovskii Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia;2.Ural Federal University,Yekaterinburg,Russia;3.Ural State University of Economics,Yekaterinburg,Russia |
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| Abstract: | The following results are obtained: (1) a criterion for the separability of the space of continuous functions C(X) with the set-open topology; (2) a criterion for the sequential separability of the space Cp(A|X), where A ? X; (3) an answer to Velichko’s question of whether a set-theoretic condition on a metric space X in a criterion for the sequential separability of Cp(X) is necessary. |
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