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Relationships Between Spaces and Their Functional Generators

Yuschik, Alex (2024) Relationships Between Spaces and Their Functional Generators. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Yuschik, Alexahy5@pitt.eduahy5
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairGartside, Paulpmg20@pitt.edupmg20
Committee MemberDeBlois, Jasonjdeblois@pitt.edujdeblois
Committee MemberLennard, Christopherlennard@pitt.edulennard
Committee MemberNyikos,
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


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