Daniel Soukup
Published 2010-02-12, updated 2010-04-18Version 3
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.
Comments: 17 pages, corrected, restructured and extended with a stronger result
Certain properties of contra-T*12-continuous functions
On some properties of the space of upper semicontinuous functions
Selection principles related to $α_i$-properties
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