Extending Topological Abelian Groups by the Unit Circle
Joint Authors
Bello, Hugo J.
Chasco, María Jesús
Domínguez, Xabier
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-27
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
A twisted sum in the category of topological Abelian groups is a short exact sequence 0→Y→X→Z→0 where all maps are assumed to be continuous and open onto their images.
The twisted sum splits if it is equivalent to 0→Y→Y×Z→Z→0.
We study the class STG? of topological groups G for which every twisted sum 0→?→X→G→0 splits.
We prove that this class contains Hausdorff locally precompact groups, sequential direct limits of locally compact groups, and topological groups with ℒ∞ topologies.
We also prove that it is closed by taking open and dense subgroups, quotients by dually embedded subgroups, and coproducts.
As means to find further subclasses of STG?, we use the connection between extensions of the form 0→?→X→G→0 and quasi-characters on G, as well as three-space problems for topological groups.
The subject is inspired on some concepts known in the framework of topological vector spaces such as the notion of ?-space, which were interpreted for topological groups by Cabello.
American Psychological Association (APA)
Bello, Hugo J.& Chasco, María Jesús& Domínguez, Xabier. 2013. Extending Topological Abelian Groups by the Unit Circle. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-483200
Modern Language Association (MLA)
Bello, Hugo J.…[et al.]. Extending Topological Abelian Groups by the Unit Circle. Abstract and Applied Analysis No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-483200
American Medical Association (AMA)
Bello, Hugo J.& Chasco, María Jesús& Domínguez, Xabier. Extending Topological Abelian Groups by the Unit Circle. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-483200
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-483200