Poerio, Thomas
(2008)
Topological Algebraic Structure in the Density Topology and on Souslin Lines.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
This research investigates which topological algebraic structures can exist on two types of topological spaces: the real line R with the density topology; and any linearly ordered topological space (LOTS) satisfying the countable chain condition (CCC) that is not separable (i.e. any Souslin Line). Some surprising results are established in the density topology when considering the common group operations on R. Indeed, this research shows that addition and multiplication are not topological group operations in this space. These theorems are then generalized to show that there are no topological group operations on R with the density topology. The case of cancellative topological semigroups, however, is left as an open question.On the other hand, the conditions of existence of topological algebraic structures on Souslin lines is rather completely determined by this work. The main results in this space are that paratopological groups do not exist on any Souslin line, but cancellative topological semigroups do exist. The research on this space culminates with the construction of a cancellative topological semigroup on a Souslin line.
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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Unpublished |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: |
3 November 2008 |
| Date Type: |
Completion |
| Defense Date: |
30 July 2008 |
| Approval Date: |
3 November 2008 |
| Submission Date: |
6 August 2008 |
| 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: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
group; paratopological group; semigroup; Souslin; Suslin; topological algebra; topological group; topological semigroup |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-08062008-122955/, etd-08062008-122955 |
| Date Deposited: |
10 Nov 2011 19:57 |
| Last Modified: |
15 Nov 2016 13:48 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/8942 |
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