Spaces with large relative extent |
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Authors: | Yan-Kui Song |
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Institution: | (1) Department of Mathematics, Nanjing Normal University, Nanjing, 210097, P.R. China |
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Abstract: | In this paper, we prove the following statements: (1) For every regular uncountable cardinal κ, there exist a Tychonoff space X and Y a subspace of X such that Y is both relatively absolute star-Lindelöf and relative property (a) in X and e(Y, X) ? κ, but Y is not strongly relative star-Lindelöf in X and X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly relative star-Lindelöf in X (hence, relative star-Lindelöf), but Y is not absolutely relative star-Lindelöf in X. |
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Keywords: | relative topological property Lindel?f star-Lindel?f relative extent relative property (a) |
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