Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-29T18:19:35.374Z Has data issue: false hasContentIssue false
  • English
  • Français

Generators on the arc component of compact connected groups

Published online by Cambridge University Press:  24 October 2008

Karl H. Hofmann  and
Sidney A. Morris
Karl H. Hofmann
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D-6100 Darmstadt, Germany
Sidney A. Morris
Affiliation:
Faculty of Informatics, University of Wollongong, Wollongong, NSW 2522, Australia
Get access Rights & Permissions [Opens in a new window]

Extract

It is well-known that a compact connected abelian group G has weight w(G) less than or equal to the cardinality c of the continuum if and only if it is monothetic; that is, if and only if it can be topologically generated by one element. Hofmann and Morris [2] extended this by showing that a compact connected (not necessarily abelian) group can be topologically generated by two elements if and only if w(G) ≤ c.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 479 - 486
Copyright
Copyright © Cambridge Philosophical Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Hofmann, K. H. and Morris, S. A.. Free compact groups I: Free compact abelian groups. Topology Appl. 23(1986), 41–64CrossRefGoogle Scholar
Errata, Topology Appl. 28 (1988), 101–102.CrossRefGoogle Scholar
[2]Hofmann, K. H. and Morris, S. A.. Weight and c. J. Pure Appl. Algebra 68 (1990), 181–194.CrossRefGoogle Scholar
[3]Hofmann, K. H. and Morris, S. A.. Free compact groups III: Free semisimple compact groups. In Proceedings of the Categorical Topology conference, Prague, August 1988 (editors Adámek, J. and MacLane, S.), (World Scientific Publishers 1989), pp. 208–219.Google Scholar
[4]Hofmann, K. H., Wu, T. S. and Yang, J. S.. Equidimensional immersions of locally compact groups. Math. Proc. Cambridge Philos. Soc. 105 (1989), 253–261.CrossRefGoogle Scholar
[5]Iwasawa, K.. On some types of topological groups. Ann. of Math. 50 (1949), 507–558.CrossRefGoogle Scholar