Properties D and aD are different

Abstract

Under $({♢}^{\ast })$ 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.

17 pages, corrected, restructured and extended with a stronger result

Cited by in corpus (1)

• Guessing clubs for aD, non D-spaces