Properties D and aD are different

Daniel Soukup

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arXiv · 1002.2585

Properties D and aD are different

Daniel Soukup

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Abstract

Under $(\diamondsuit^*)$ we construct a locally countable, locally compact, 0-dimensional $T_2$ space $X$ of size $\omg$ which is aD however not even linearly D. This consistently answers a question of Arhangel'skii, whether aD implies D. Furthermore we answer two problems concerning characterization of linearly D-spaces, raised by Guo and Junnila.

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Daniel Soukup. 2010-04-18. Properties D and aD are different. https://arxiv.org/abs/1002.2585

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