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Spaces with large relative extent

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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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  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, P.R. China

    Yan-Kui Song

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  1. Yan-Kui Song
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Song, YK. Spaces with large relative extent. Czech Math J 57, 387–394 (2007). https://doi.org/10.1007/s10587-007-0067-3

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  • DOI: https://doi.org/10.1007/s10587-007-0067-3

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