Date of Award

1-1-2011

Document Type

Campus Access Dissertation

Department

Mathematics

First Advisor

Peter J Nyikos

Abstract

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.

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]α 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 < ω1 the author shows that any L-special tree is a D-space. For the remaining countable ordinals α, the current progress is shown.

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