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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
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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

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References

REFERENCES

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