Constructing aD, non- D-spaces

We introduce a general method to construct 0-dimensional, scattered T 2 spaces which are not linearly D. The construction is used to show that there are aD, non- D-spaces, answering a question of Arhangelʼskii. The latter example is achieved using Shelahʼs club guessing principles.

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Bibliographic Details
Published inTopology and its applications Vol. 158; no. 10; pp. 1219 - 1225
Main Author Soukup, Dániel Tamás
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.06.2011
Subjects
aD-spaces
Club guessing
D-spaces
54D20
D-spaces
03E75
aD-spaces
Club guessing
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Summary:We introduce a general method to construct 0-dimensional, scattered T 2 spaces which are not linearly D. The construction is used to show that there are aD, non- D-spaces, answering a question of Arhangelʼskii. The latter example is achieved using Shelahʼs club guessing principles.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2011.04.008