Convergent nets in abelian topological groups
A net in an abelian group is called a T-net if there exists a Hausdorff group topology in which the net converges to 0. This paper describes a fundamental system for the finest group topology in which the net converges to 0. The paper uses this description to develop conditions which insure there ex...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120100744X |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567838426005504 |
|---|---|
| author | Robert Ledet |
| author_facet | Robert Ledet |
| author_sort | Robert Ledet |
| collection | DOAJ |
| description | A net in an abelian group is called a T-net if there exists a Hausdorff group topology in which the net converges to 0. This
paper describes a fundamental system for the finest group
topology in which the net converges to 0. The paper uses this
description to develop conditions which insure there exists a
Hausdorff group topology in which a particular subgroup is dense
in a group. Examples given include showing that there are
Hausdorff group topologies on ℝn in which any
particular axis may be dense and Hausdorff group topologies on
the torus in which S1 is dense. |
| format | Article |
| id | doaj-art-f8bad262d5a242039ac88926527131f9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f8bad262d5a242039ac88926527131f92025-02-03T01:00:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01271164565110.1155/S016117120100744XConvergent nets in abelian topological groupsRobert Ledet0200 Wingfield Drive, Houma, LA 70360, USAA net in an abelian group is called a T-net if there exists a Hausdorff group topology in which the net converges to 0. This paper describes a fundamental system for the finest group topology in which the net converges to 0. The paper uses this description to develop conditions which insure there exists a Hausdorff group topology in which a particular subgroup is dense in a group. Examples given include showing that there are Hausdorff group topologies on ℝn in which any particular axis may be dense and Hausdorff group topologies on the torus in which S1 is dense.http://dx.doi.org/10.1155/S016117120100744X |
| spellingShingle | Robert Ledet Convergent nets in abelian topological groups International Journal of Mathematics and Mathematical Sciences |
| title | Convergent nets in abelian topological groups |
| title_full | Convergent nets in abelian topological groups |
| title_fullStr | Convergent nets in abelian topological groups |
| title_full_unstemmed | Convergent nets in abelian topological groups |
| title_short | Convergent nets in abelian topological groups |
| title_sort | convergent nets in abelian topological groups |
| url | http://dx.doi.org/10.1155/S016117120100744X |
| work_keys_str_mv | AT robertledet convergentnetsinabeliantopologicalgroups |