Properties D and aD are different
General Topology
2010-04-20 v3
Abstract
Under we construct a locally countable, locally compact, 0-dimensional space of size 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.
Cite
@article{arxiv.1002.2585,
title = {Properties D and aD are different},
author = {Daniel Soukup},
journal= {arXiv preprint arXiv:1002.2585},
year = {2010}
}
Comments
17 pages, corrected, restructured and extended with a stronger result