This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
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
Date of Ingest
2011-05-07T12:14:05Z
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.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
