Algebraic Characterization of Dense-Separability Among Compact Spaces |
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| Authors: | Ehsan Momtahan |
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| Institution: | 1. Department of Mathematics , Yasuj University , Yasuj, Iran;2. Institute for Studies in Theoretical Physics and Mathematics (IPM) e-momtahan@mail.yu.ac.ir;5. momtahan-e@hotmail.com |
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| Abstract: | In this note, we show that a compact Hausdorff space X is dense-separable if and only if every family of ideals of C(X) with zero intersection has a countable subfamily with zero intersection. As a consequence of this characterization we observe that every compact dense-separable space whith Soc(C(X)) = 0 has a countable dense and co-dense subset. |
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| Keywords: | Alpha-cogenerated ring Dense-separable space Socle |
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