Around a Quotient Space of Bennett-Lutzer’s Space Acerca de un Espacio Cociente del Espacio de Bennett-Lutzer
نویسنده
چکیده
Let X be the Bennett-Lutzer’s space and Y be the space obtained from X by shrinking the set of all rational numbers to a point. In his book, G.Gao claimed that the space Y is compact. In this paper, we prove that Y is neither countably compact nor Lindelöf, which shows that G.Gao’s claim is not true. Moreover, we prove that Y is strongly paracompact. As an application of this result, we obtain that all covering properties which are between strong paracompactness and countable θ-refinability are not inversely preserved under closed Lindelöf mappings even if domain is Hausdorff. We also give an example to show that a closed Lindelöf inverse image of a compact space even need not be countably θ-refinable without requiring the regularity of domain involved.
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