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https://hdl.handle.net/2142/19648
Description
Title
O-minimal homology
Author(s)
Woerheide, Arthur Anderson
Issue Date
1996
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
The purpose of this dissertation is to define homology functors for the category of definable sets and definable continuous maps in an o-minimal expansion of an ordered field. Both simplicial and singular homology functors are defined, and they are shown to satisfy the Eilenberg-Steenrod axioms. The singular homology functor is used to prove o-minimal analogues of the Jordan-Brouwer separation theorem and Brouwer's invariance of domain theorem.
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