The D-property of some Lindelöf spaces and related conclusions |
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Authors: | Liang-Xue Peng |
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Institution: | College of Applied Science, Beijing University of Technology, Beijing 100022, China |
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Abstract: | It is shown that the space Cp(τω) is a D-space for any ordinal number τ, where . This conclusion gives a positive answer to R.Z. Buzyakova's question. We also prove that another special example of Lindelöf space is a D-space. We discuss the D-property of spaces with point-countable weak bases. We prove that if a space X has a point-countable weak base, then X is a D-space. By this conclusion and one of T. Hoshina's conclusion, we have that if X is a countably compact space with a point-countable weak base, then X is a compact metrizable space. In the last part, we show that if a space X is a finite union of θ-refinable spaces, then X is a αD-space. |
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Keywords: | 54C35 54D20 54F05 |
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