Bedich, Joseph
(2024)
Combinatorics of Finite Open Covers.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Given any graph or simplicial invariant $f$, we can define an analogous topological invariant and determine its values for a given topological space $X$. These topological invariants are defined by applying the graph or simplicial invariant $f$ to the nerves of finite open covers of $X$. In this work, we discuss how to define such topological invariants, and we analyze several topological invariants that correspond to classical graph invariants. We also define and investigate the related notion of forced substructures of a topological space. Lastly, we investigate topological invariants that correspond to a particular class of graph invariants known as minor-monotone invariants.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
|
| Date: |
27 August 2024 |
| Date Type: |
Publication |
| Defense Date: |
18 July 2024 |
| Approval Date: |
27 August 2024 |
| Submission Date: |
24 July 2024 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
154 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
topology, graph theory, topological invariant, graph invariant, simplicial complex, nerve, open cover, continua theory |
| Date Deposited: |
27 Aug 2024 13:33 |
| Last Modified: |
27 Aug 2024 13:33 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/46736 |
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