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Invariant means and fixed point properties on completely regular spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
Two theorems are presented which characterize the existence of multiplicative left invariant means on a given algebra of unbounded continuous functions on a topological semigroup S in terms of certain common fixed point properties of actions of S on completely regular spaces. Also a lattice formulation of a related result of Theodore Mitchell for the case of bounded functions is shown to be equivalent to a certain common fixed point property on Bauer simplexes.
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- Copyright © Australian Mathematical Society 1977