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Topics in general and set-theoretic topology: slice sets, rigid subsets of the reals, Toronto spaces, cleavability, and neight

Abstract:

I explore five topics in topology using set-theoretic techniques. The first of these is a generalization of 2-point sets called slice sets. I show that, for any small-in-cardinality subset A of the real line, there is a subset of the plane meeting every line in a topological copy of A. Under Martin's Axiom, I show how to improve this result to any totally disconnected A. Secondly, I show that it is consistent with and independent of ZFC to have a topologically rigid subset of the real line...

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Institution:
University of Oxford
Research group:
Logic; Analytic Topology
Oxford college:
Trinity College
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute
Role:
Author

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Funding agency for:
William R. Brian
Publication date:
2013
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
Oxford University, UK
URN:
uuid:d80b6234-91e4-4c80-8696-a6de7aabc985
Local pid:
ora:7467

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