Geodesic
Ergodic sets and mixing extensions of topological transformation semigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 87-94
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We extend the concept of the ergodic set [1]–[2] from topological transformation groups to topological transformation semigroups. We investigate, in particular, connections between ergodicity, weak ergodicity, topological transitivity and minimality of the Whitney's sum of extensions of topological transformation semigroups. 
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A. I. Gherco. Ergodic sets and mixing extensions of topological transformation semigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2003), pp. 87-94. http://geodesic.mathdoc.fr/item/BASM_2003_2_a7/

[1] Furstenberg H., “Disjointness in Ergodic Theory, Minimal Sets, and a Problem in Diophantine Approximation”, Math. Systems Theory, 1 (1967), 1–50 | DOI | MR

[2] Woude J. C. S. P., van der, Topological dynamics, Mathematisch Centrum, Amsterdam, 1982

[3] Bronstein I. U., Rasshirenia minimalnyh grupp preobrazovanii, RIO ANMSSR, Kishinev, 1975; Extensions of Minimal Transformation Groups, Sijthoff Noordhoff International Publishers, 1979 | MR

[4] Bronstein I. U., Gherco A. I., “O vlozenii nekotoryh topologiceskih polugrupp preobrazovanii v topologiceskie gruppy preobrazovanii”, Izv. AN MSSR, seria fiz.-tehn. i matem. nauk, 3 (1970), 18–24 | MR

[5] Gherco A. I., Rasshirenia topologiceskih polugrupp preobrazovanii, Izdatelskii tsentr Mold. gosuniversiteta, Kishinev, 2001