A compact monothetic semitopological semigroup whose set of idempotents is not closed

Ahmed Bouziad (1) , Mariusz Lemanczyk (2, 3, 4) , Mieczys?aw K. Mentzen

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 Faculty of Mathematics and Computer Sciences
3 Faculty of Mathematics and Computer Science
4 Faculty of Mathematics and Computer Science and Institute of Mathematics

For each monothetic unitary group without proper co-compact subgroups, we show the existence of a compact semitopological semigroup (affine) compactification in which the set of idempotents is not closed, answering a question of J. F. Berglund [Semigroup Forum 19 (1980), no. 4, 373--383]

Mots clés: integers; weacly almost periodic compactification; idempotent

Domaines: Systèmes dynamiques [math.DS]

Ahmed Bouziad, Mariusz Lemanczyk, Mieczys?aw K. Mentzen. A compact monothetic semitopological semigroup whose set of idempotents is not closed. Semigroup Forum, 2001, 62 (1), pp.98--102. ⟨hal-00373440⟩