Mastros, Sara Leanne
(2009)
S and L Spaces.
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
An S-space is any topological space which is hereditarily separable but not Lindelof. An L-space, on the other hand, is hereditarily Lindelof but not separable. For almost a century, determining the necessary and suffcient conditions for the existence of these two kinds of spaces has been a fruitful area of research at the boundary of topology and axiomatic set theory. For most of that time, the twoproblems were imagined to be dual; that is, it was believed that the same setsof conditions that required or precluded one type would suffice for the other aswell. This, however, is not the case. When Todorcevic proved in 1981 that itis consistent, under ZFC, for no S-spaces to exist, everyone expected a similarresult to follow for L-spaces as well. Justin Tatch Moore surprised everyonewhen, in 2005, he constructed an L-space in ZFC. This paper summarizes andcontextualizes that result, along with several others in the field.
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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Unpublished |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: |
29 September 2009 |
| Date Type: |
Completion |
| Defense Date: |
12 June 2009 |
| Approval Date: |
29 September 2009 |
| Submission Date: |
10 July 2009 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
MS - Master of Science |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
l spaces; s spaces; Set Theory; souslin; suslin; tatch moore; Topology |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-07102009-140053/, etd-07102009-140053 |
| Date Deposited: |
10 Nov 2011 19:50 |
| Last Modified: |
15 Nov 2016 13:45 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/8332 |
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