Hindman, N and Strauss, D (2017) Topological properties of some algebraically defined subsets of βN. Topology and its Applications, 220. pp. 43-49. ISSN 0166-8641
Abstract
Let S be a discrete semigroup and let the Stone–Čech compactification βS of S have the operation extending that of S which makes βS a right topological semigroup with S contained in its topological center. We show that the closure of the set of multiplicative idempotents in β N does not meet the set of additive idempotents in β N . We also show that the following algebraically defined subsets of β N are not Borel: the set of idempotents; the smallest ideal; any semiprincipal right ideal of N ⁎ ; the set of idempotents in any left ideal; and N ⁎ + N ⁎ . We extend these results to βS, where S is an infinite countable semigroup algebraically embeddable in a compact topological group.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Published by Elsevier B.V. This is an author produced version of a paper published in Topology and its Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Stone–Čech compactification; Idempotent; Borel |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Feb 2017 11:17 |
Last Modified: | 08 Feb 2018 01:38 |
Published Version: | https://doi.org/10.1016/j.topol.2017.02.001 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.topol.2017.02.001 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:112168 |