Yuschik, Alex
(2024)
Relationships Between Spaces and Their Functional Generators.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
A subset $G$ of the set $C(X)$ of all continuous real valued functions on a Tychonoff space $X$, is a \emph{generator} if
whenever $x$ is a point of $X$ not in a closed set $C$ then there is a $g$ in $G$ such that $g(x) \notin \cl{g(C)}$.
The set $C(X)$ admits some natural topologies, including the topology of pointwise convergence and the compact open topology.
Generators, then, are subspaces of these function spaces.
In this work, we examine discrete, compact and first and second countable generators.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
7 February 2024 |
| Date Type: |
Publication |
| Defense Date: |
11 August 2021 |
| Approval Date: |
7 February 2024 |
| Submission Date: |
9 September 2021 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
77 |
| 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, generators, function spaces, countability, discreteness, compactness |
| Date Deposited: |
07 Feb 2024 19:35 |
| Last Modified: |
07 Feb 2024 19:35 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/41781 |
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