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A One-Parameter Subsemigroup which meets many Regular
-Classes
Published online by Cambridge University Press: 20 November 2018
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We give an example which answers affirmatively the following problem posed by Hofmann and Mostert (1, p. 200):
P. 10. Let S be a compact semigroup with identity 1, zero 0, and totally ordered -class space
. Suppose that there is a one-parameter semigroup containing 0 and 1. Can S have any regular
-classes aside from D(0) and D(1)?
I am indebted to Professor K. H. Hofmann and Professor P. S. Mostert for their many helpful suggestions.
1. We first give a method of embedding a given semigroup S in a semigroup R so that in the commutative diagram
the bottom map is an isomorphism of partially ordered spaces and some non-regular -class of S is embedded into a regular
-class of R.
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- Copyright © Canadian Mathematical Society 1969