Generators on the arc component of compact connected groups Academic Article uri icon

abstract

  • 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.

publication date

  • May 1993