Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-7x8lp Total loading time: 0.253 Render date: 2021-03-06T06:21:02.444Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Type-definable and invariant groups in o-minimal structures

Published online by Cambridge University Press:  12 March 2014

Jana Maříková
Affiliation:
Department of Mathematics, University of Illinois, Urbana-Champaign, 257 Altgeld Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: marikova@math.uiuc.edu
Corresponding
E-mail address:

Abstract

Let M be a big o-minimal structure and G a type-definable group in Mn. We show that G is a type-definable subset of a definable manifold in Mn that induces on G a group topology. If M is an o-minimal expansion of a real closed field, then G with this group topology is even definably isomorphic to a type-definable group in some Mk with the topology induced by Mk. Part of this result holds for the wider class of so-called invariant groups: each invariant group G in Mn has a unique topology making it a topological group and inducing the same topology on a large invariant subset of the group as Mn.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2007

Access options

Get access to the full version of this content by using one of the access options below.

References

[1]Berarducci, A. and Otero, M., Intersection theory for o-minimal manifolds. Annals of Pure and Applied Logic, vol. 107 (2001), no. 1-3, pp. 87–119.CrossRefGoogle Scholar
[2]Bourbaki, N., Elements of mathematics, general topology, vol. 293, Hermann, Paris.Google Scholar
[3]Peterzil, Y. and Starchenko, S., Definable homomorphisms of abelian groups in o-minimal structures, Annals of Pure and Applied Logic, vol. 101 (2000), pp. 1–27.Google Scholar
[4]Pillay, A., On groups and fields definable in o-minimal structures, Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239–255.CrossRefGoogle Scholar
[5]van den Dries, L., Tame topology and o-minimal structures, London Mathematical Society Lecture Note Series, vol. 248, Cambridge University Press, Cambridge, 1998.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 14 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 6th March 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Type-definable and invariant groups in o-minimal structures
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Type-definable and invariant groups in o-minimal structures
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Type-definable and invariant groups in o-minimal structures
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *