The D-property in unions of scattered spaces |
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Authors: | Juan Carlos Martínez Lajos Soukup |
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Institution: | a Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain b Alfréd Rényi Institute of Mathematics, Budapest, Hungary |
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Abstract: | We show in a direct way that a space is D if it is a finite union of subparacompact scattered spaces. This result cannot be extended to countable unions, since it is known that there is a regular space which is a countable union of paracompact scattered spaces and which is not D. Nevertheless, we show that every space which is the union of countably many regular Lindelöf C-scattered spaces has the D-property. Also, we prove that a space is D if it is a locally finite union of regular Lindelöf C-scattered spaces. |
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Keywords: | 54D20 54G12 91A44 |
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