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S and L Spaces

Mastros, Sara Leanne (2009) S and L Spaces. Master's Thesis, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Mastros, Sara
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairGartside, Paulgartside@math.pitt.eduPMG20
Committee MemberEspinoza,
Committee MemberHeath, Bobrwheath@pitt.eduRWHEATH
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:, etd-07102009-140053
Date Deposited: 10 Nov 2011 19:50
Last Modified: 15 Nov 2016 13:45


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