Geodesic
A One-Parameter Subsemigroup which meets many Regular -Classes
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 735-739

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Tymchatyn, E. D. A One-Parameter Subsemigroup which meets many Regular -Classes. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 735-739. doi: 10.4153/CJM-1969-082-x
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[1] 1. Hofmann, K. H. and Mostert, P. S., Elements of compact semigroups (Charles E. Merrill Books, Columbus, Ohio, 1966). Google Scholar

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