On D-Paracompact spaces |
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Authors: | Harald Brandenburg |
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Institution: | Institut für Mathematik I, Freie Universität Berlin, Berlin, Federal Republic of Germany |
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Abstract: | Following Pareek a topological space X is called D-paracompact if for every open cover of X there exists a continuous mapping f from X onto a developable T1-space Y and an open cover of Y such that { f-1B]|B ∈ } refines . It is shown that a space is D-paracompact if and only if it is subparacompact and D-expandable. Moreover, it is proved that D-paracompactness coincides with a covering property, called dissectability, which was introduced by the author in order to obtain a base characterization of developable spaces. |
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Keywords: | Primary 54D18 Secondary: 54D20 54E30 54E25 |
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