English

Properties D and aD are different

General Topology 2010-04-20 v3

Abstract

Under ()(\diamondsuit^*) we construct a locally countable, locally compact, 0-dimensional T2T_2 space XX of size \omg\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.

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

R2 v1 2026-06-21T14:46:31.597Z