---
_id: '64634'
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Completeness of locally k_ω-groups and related infinite-dimensional
    Lie groups. <i>Topology and its Applications</i>. 2017;228:277–284. doi:<a href="https://doi.org/10.1016/j.topol.2017.05.007">10.1016/j.topol.2017.05.007</a>
  apa: Glöckner, H. (2017). Completeness of locally k_ω-groups and related infinite-dimensional
    Lie groups. <i>Topology and Its Applications</i>, <i>228</i>, 277–284. <a href="https://doi.org/10.1016/j.topol.2017.05.007">https://doi.org/10.1016/j.topol.2017.05.007</a>
  bibtex: '@article{Glöckner_2017, title={Completeness of locally k_ω-groups and related
    infinite-dimensional Lie groups}, volume={228}, DOI={<a href="https://doi.org/10.1016/j.topol.2017.05.007">10.1016/j.topol.2017.05.007</a>},
    journal={Topology and its Applications}, author={Glöckner, Helge}, year={2017},
    pages={277–284} }'
  chicago: 'Glöckner, Helge. “Completeness of Locally K_ω-Groups and Related Infinite-Dimensional
    Lie Groups.” <i>Topology and Its Applications</i> 228 (2017): 277–284. <a href="https://doi.org/10.1016/j.topol.2017.05.007">https://doi.org/10.1016/j.topol.2017.05.007</a>.'
  ieee: 'H. Glöckner, “Completeness of locally k_ω-groups and related infinite-dimensional
    Lie groups,” <i>Topology and its Applications</i>, vol. 228, pp. 277–284, 2017,
    doi: <a href="https://doi.org/10.1016/j.topol.2017.05.007">10.1016/j.topol.2017.05.007</a>.'
  mla: Glöckner, Helge. “Completeness of Locally K_ω-Groups and Related Infinite-Dimensional
    Lie Groups.” <i>Topology and Its Applications</i>, vol. 228, 2017, pp. 277–284,
    doi:<a href="https://doi.org/10.1016/j.topol.2017.05.007">10.1016/j.topol.2017.05.007</a>.
  short: H. Glöckner, Topology and Its Applications 228 (2017) 277–284.
date_created: 2026-02-26T07:21:22Z
date_updated: 2026-02-27T08:33:12Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1016/j.topol.2017.05.007
intvolume: '       228'
keyword:
- '22E65'
- 22A05
- 46A13
- 46M40
- 58D05
language:
- iso: eng
page: 277–284
publication: Topology and its Applications
publication_identifier:
  issn:
  - 0166-8641
quality_controlled: '1'
status: public
title: Completeness of locally k_ω-groups and related infinite-dimensional Lie groups
type: journal_article
user_id: '178'
volume: 228
year: '2017'
...
---
_id: '64672'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Upper bounds for continuous seminorms and special properties of
    bilinear maps. <i>Topology and its Applications</i>. 2012;159(13):2990–3001. doi:<a
    href="https://doi.org/10.1016/j.topol.2012.05.010">10.1016/j.topol.2012.05.010</a>
  apa: Glöckner, H. (2012). Upper bounds for continuous seminorms and special properties
    of bilinear maps. <i>Topology and Its Applications</i>, <i>159</i>(13), 2990–3001.
    <a href="https://doi.org/10.1016/j.topol.2012.05.010">https://doi.org/10.1016/j.topol.2012.05.010</a>
  bibtex: '@article{Glöckner_2012, title={Upper bounds for continuous seminorms and
    special properties of bilinear maps}, volume={159}, DOI={<a href="https://doi.org/10.1016/j.topol.2012.05.010">10.1016/j.topol.2012.05.010</a>},
    number={13}, journal={Topology and its Applications}, author={Glöckner, Helge},
    year={2012}, pages={2990–3001} }'
  chicago: 'Glöckner, Helge. “Upper Bounds for Continuous Seminorms and Special Properties
    of Bilinear Maps.” <i>Topology and Its Applications</i> 159, no. 13 (2012): 2990–3001.
    <a href="https://doi.org/10.1016/j.topol.2012.05.010">https://doi.org/10.1016/j.topol.2012.05.010</a>.'
  ieee: 'H. Glöckner, “Upper bounds for continuous seminorms and special properties
    of bilinear maps,” <i>Topology and its Applications</i>, vol. 159, no. 13, pp.
    2990–3001, 2012, doi: <a href="https://doi.org/10.1016/j.topol.2012.05.010">10.1016/j.topol.2012.05.010</a>.'
  mla: Glöckner, Helge. “Upper Bounds for Continuous Seminorms and Special Properties
    of Bilinear Maps.” <i>Topology and Its Applications</i>, vol. 159, no. 13, 2012,
    pp. 2990–3001, doi:<a href="https://doi.org/10.1016/j.topol.2012.05.010">10.1016/j.topol.2012.05.010</a>.
  short: H. Glöckner, Topology and Its Applications 159 (2012) 2990–3001.
date_created: 2026-02-26T11:04:46Z
date_updated: 2026-02-27T08:25:06Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1016/j.topol.2012.05.010
intvolume: '       159'
issue: '13'
keyword:
- 46A03
- 46F05
- 22D15
- 42A85
- 46A11
- 46A32
language:
- iso: eng
page: 2990–3001
publication: Topology and its Applications
publication_identifier:
  issn:
  - 0166-8641
quality_controlled: '1'
status: public
title: Upper bounds for continuous seminorms and special properties of bilinear maps
type: journal_article
user_id: '178'
volume: 159
year: '2012'
...
---
_id: '64673'
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
- first_name: Bastian
  full_name: Langkamp, Bastian
  last_name: Langkamp
citation:
  ama: Glöckner H, Langkamp B. Topological algebras of rapidly decreasing matrices
    and generalizations. <i>Topology and its Applications</i>. 2012;159(9):2420–2422.
    doi:<a href="https://doi.org/10.1016/j.topol.2011.09.048">10.1016/j.topol.2011.09.048</a>
  apa: Glöckner, H., &#38; Langkamp, B. (2012). Topological algebras of rapidly decreasing
    matrices and generalizations. <i>Topology and Its Applications</i>, <i>159</i>(9),
    2420–2422. <a href="https://doi.org/10.1016/j.topol.2011.09.048">https://doi.org/10.1016/j.topol.2011.09.048</a>
  bibtex: '@article{Glöckner_Langkamp_2012, title={Topological algebras of rapidly
    decreasing matrices and generalizations}, volume={159}, DOI={<a href="https://doi.org/10.1016/j.topol.2011.09.048">10.1016/j.topol.2011.09.048</a>},
    number={9}, journal={Topology and its Applications}, author={Glöckner, Helge and
    Langkamp, Bastian}, year={2012}, pages={2420–2422} }'
  chicago: 'Glöckner, Helge, and Bastian Langkamp. “Topological Algebras of Rapidly
    Decreasing Matrices and Generalizations.” <i>Topology and Its Applications</i>
    159, no. 9 (2012): 2420–2422. <a href="https://doi.org/10.1016/j.topol.2011.09.048">https://doi.org/10.1016/j.topol.2011.09.048</a>.'
  ieee: 'H. Glöckner and B. Langkamp, “Topological algebras of rapidly decreasing
    matrices and generalizations,” <i>Topology and its Applications</i>, vol. 159,
    no. 9, pp. 2420–2422, 2012, doi: <a href="https://doi.org/10.1016/j.topol.2011.09.048">10.1016/j.topol.2011.09.048</a>.'
  mla: Glöckner, Helge, and Bastian Langkamp. “Topological Algebras of Rapidly Decreasing
    Matrices and Generalizations.” <i>Topology and Its Applications</i>, vol. 159,
    no. 9, 2012, pp. 2420–2422, doi:<a href="https://doi.org/10.1016/j.topol.2011.09.048">10.1016/j.topol.2011.09.048</a>.
  short: H. Glöckner, B. Langkamp, Topology and Its Applications 159 (2012) 2420–2422.
date_created: 2026-02-26T11:06:13Z
date_updated: 2026-02-27T08:24:38Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: 10.1016/j.topol.2011.09.048
intvolume: '       159'
issue: '9'
keyword:
- 46H20
- 46A45
- '22E65'
language:
- iso: eng
page: 2420–2422
publication: Topology and its Applications
publication_identifier:
  issn:
  - 0166-8641
quality_controlled: '1'
status: public
title: Topological algebras of rapidly decreasing matrices and generalizations
type: journal_article
user_id: '178'
volume: 159
year: '2012'
...
---
_id: '64691'
abstract:
- lang: eng
  text: We show that countable direct limits of finite-dimensional Lie groups do not
    have small subgroups. The same conclusion is obtained for suitable direct limits
    of infinite-dimensional Lie groups.
article_type: original
author:
- first_name: Helge
  full_name: Glöckner, Helge
  id: '178'
  last_name: Glöckner
citation:
  ama: Glöckner H. Direct limit groups do not have small subgroups. <i>Topology and
    its Applications</i>. 2007;154(6):1126-1133. doi:<a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>
  apa: Glöckner, H. (2007). Direct limit groups do not have small subgroups. <i>Topology
    and Its Applications</i>, <i>154</i>(6), 1126–1133. <a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>
  bibtex: '@article{Glöckner_2007, title={Direct limit groups do not have small subgroups},
    volume={154}, DOI={<a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>},
    number={6}, journal={Topology and its Applications}, author={Glöckner, Helge},
    year={2007}, pages={1126–1133} }'
  chicago: 'Glöckner, Helge. “Direct Limit Groups Do Not Have Small Subgroups.” <i>Topology
    and Its Applications</i> 154, no. 6 (2007): 1126–33. <a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>.'
  ieee: 'H. Glöckner, “Direct limit groups do not have small subgroups,” <i>Topology
    and its Applications</i>, vol. 154, no. 6, pp. 1126–1133, 2007, doi: <a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>.'
  mla: Glöckner, Helge. “Direct Limit Groups Do Not Have Small Subgroups.” <i>Topology
    and Its Applications</i>, vol. 154, no. 6, 2007, pp. 1126–33, doi:<a href="https://doi.org/10.1016/j.topol.2006.11.003">https://doi.org/10.1016/j.topol.2006.11.003</a>.
  short: H. Glöckner, Topology and Its Applications 154 (2007) 1126–1133.
date_created: 2026-02-26T11:43:06Z
date_updated: 2026-02-26T11:44:04Z
department:
- _id: '10'
- _id: '87'
- _id: '93'
doi: https://doi.org/10.1016/j.topol.2006.11.003
extern: '1'
intvolume: '       154'
issue: '6'
keyword:
- Infinite-dimensional Lie group
- Direct limit group
- Direct limit
- Inductive limit
- Small subgroup
- Torsion subgroup
language:
- iso: eng
page: 1126-1133
publication: Topology and its Applications
publication_identifier:
  issn:
  - 0166-8641
quality_controlled: '1'
status: public
title: Direct limit groups do not have small subgroups
type: journal_article
user_id: '178'
volume: 154
year: '2007'
...