Abstract
dc:descriptionThe 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2011
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Woerheide, Arthur Anderson
Subjects
dc:subject × 1Rights
dc:rights- Statement dc:rights
-
- Copyright 1996 Woerheide, Arthur Anderson
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
-
9780591199666
AAI9712484
(UMI)AAI9712484 - OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/19648