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Generators on the arc component of compact connected groups
Published online by Cambridge University Press: 24 October 2008
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