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Nonclosed Pure Subgroups of Locally Compact Abelian Groups
| Content Provider | Scilit |
|---|---|
| Author | Takahashi, Yuji |
| Copyright Year | 1990 |
| Description | We study the existence of many nonclosed pure subgroups of nondiscrete locally compact abelian groups. It is shown that every nondiscrete locally compact abelian group has uncountably many nonclosed pure subgroups. This in particular solves a question of Armacost. It is also shown that, if $G$ is a nondiscrete locally compact abelian group and if either $G$ is a compact group or the torsion part $t\left ( G \right )$ of $G$ is nonopen, then $G$ has ${2^c}$ proper dense pure subgroups, where $c$ denotes the power of the continuum. This in particular gives a partial answer to another question of Armacost. |
| Related Links | https://www.ams.org/proc/1990-110-03/S0002-9939-1990-1021905-0/S0002-9939-1990-1021905-0.pdf |
| Ending Page | 849 |
| Page Count | 5 |
| Starting Page | 845 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2047931 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 3 |
| Volume Number | 110 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1990-11-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Pure Subgroups Abelian Group Compact Abelian Locally Compact Nonclosed Uncountably Nonopen Torsion |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
