The present paper deals with the concept of “codecomposition” of a transformation semigroup interacting with the phase semigroup. In this way, we distinguish new classes of transformation semigroups with meaningful relations, e.g., we show the class of all distal transformation semigroups ⊂, the class of all transformation semigroups decomposable into distal semigroups ⊂, and the class of all transformation semigroups (here, ⊂ is strict inclusion).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. U. Bronstein, Extensions of Minimal Transformation Groups, Sijthoff & Noordhoff (1979).
H. Chu, “Some inheritance theorems in topological dynamics,” J. London Math. Soc., 43, 168–170 (1968).
R. Ellis, Lectures on Topological Dynamics, Benjamin, New York (1969).
M. Garcia and G. H. Hedlund, “The structure of minimal sets,” Bull. Amer. Math. Soc., 54, 954–964 (1948).
E. Glasner, M. Megrelishvili, and V. V. Uspenskij, “On metrizable enveloping semigroups,” Isr. J. Math., 164, 317–332 (2008).
Sh. Glasner, “Proximal flows,” Lect. Notes Math., Springer-Verlag, Berlin (1976), Vol. 517.
W. H. Gottschalk, “Powers of homeomorphisms with almost periodic properties,” Bull. Amer. Math. Soc., 50, 222–227 (1944).
W. H. Gottschalk, “Orbit-closure decompositions and almost periodic properties,” Bull. Amer. Math. Soc., 50, 915–919 (1944).
J. J. Rotman, “An introduction to algebraic topology,” Grad. Texts Math., Springer-Verlag, New York, 119 (1988).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 11, pp. 1506–1514, November, 2013.
Rights and permissions
About this article
Cite this article
Sabbaghan, M., Shirazi, F.A.Z. & Hosseini, A. Codecomposition of a Transformation Semigroup. Ukr Math J 65, 1670–1680 (2014). https://doi.org/10.1007/s11253-014-0888-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-014-0888-9