Abstract
dc:description.abstract<p>This dissertation concerns D-spaces and set-theoretic trees. A topological space, X, is a D-space if for every neighbornet of the space there is a closed, discrete set from X whose images in the neighbornet are a cover for X. A set-theoretic tree is a poset where for any element the set of its predecessors is well-ordered.</p> <p>In this dissertation it is shown that certain L-special trees are D-spaces and some of them are hereditarily so.In particular, let L=[0,1]<super>α</super> with α a countable ordinal be given the lexicographic order. For α < ω+1, the author shows that any L-special tree is hereditarily a D-space. For certain α with ω < α < ω<sub>1</sub> the author shows that any L-special tree is a D-space. For the remaining countable ordinals α, the current progress is shown.</p>
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Campus Access Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Year
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Gamel, Heather
- Contributors dc:contributor
-
- Peter J Nyikos
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- © 2011, Heather Gamel
Identifiers
dc:identifier.*- Repository record dc:identifier
- https://scholarcommons.sc.edu/etd/1596
- OAI identifier oai:identifier
- oai:scholarcommons.sc.edu:etd-2597