Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access October 30, 2013

Boolean algebras admitting a countable minimally acting group

  • Aleksander Błaszczyk EMAIL logo , Andrzej Kucharski and Sławomir Turek
From the journal Open Mathematics

Abstract

The aim of this paper is to show that every infinite Boolean algebra which admits a countable minimally acting group contains a dense projective subalgebra.

[1] Balcar B., Błaszczyk A., On minimal dynamical systems on Boolean algebras, Comment. Math. Univ. Carolin., 1990, 31(1), 7–11 Search in Google Scholar

[2] Balcar B., Franek F., Structural properties of universal minimal dynamical systems for discrete semigroups, Trans. Amer. Math. Soc., 1997, 349(5), 1697–1724 http://dx.doi.org/10.1090/S0002-9947-97-01868-010.1090/S0002-9947-97-01868-0Search in Google Scholar

[3] Balcar B., Jech T., Zapletal J., Semi-Cohen Boolean algebras, Ann. Pure Appl. Logic, 1997, 87(3), 187–208 http://dx.doi.org/10.1016/S0168-0072(97)00009-210.1016/S0168-0072(97)00009-2Search in Google Scholar

[4] Bandlow I., On the absolutes of compact spaces with a minimally acting group, Proc. Amer. Math. Soc., 1994, 122(1), 261–264 http://dx.doi.org/10.1090/S0002-9939-1994-1246512-X10.1090/S0002-9939-1994-1246512-XSearch in Google Scholar

[5] Błaszczyk A., Irreducible images of βℕ \ℕ, Rend. Circ. Mat. Palermo, 1984, Suppl. 3, 47–54 Search in Google Scholar

[6] Geschke S., A note on minimal dynamical systems, Acta Univ. Carolin. Math. Phys., 2004, 45(2), 35–43 Search in Google Scholar

[7] Haydon R., On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math., 1974, 52(1), 23–31 10.4064/sm-52-1-23-31Search in Google Scholar

[8] Heindorf L., Shapiro L.B., Nearly Projective Boolean Algebras, Lect. Notes Math., 1596, Springer, Berlin, 1994 10.1007/BFb0094103Search in Google Scholar

[9] Koppelberg S., Handbook of Boolean Algebras, 1, North-Holland, Amsterdam, 1989 Search in Google Scholar

[10] Koppelberg S., Projective Boolean algebras, In: Handbook of Boolean Algebras, 3, North-Holland, Amsterdam, 1989, 741–773 Search in Google Scholar

[11] Koppelberg S., Characterizations of Cohen algebras, In: Papers on General Topology and Applications, Madison, 1991, Ann. New York Acad. Sci., 704, New York Acad. Sci., New York, 1993, 222–237 10.1111/j.1749-6632.1993.tb52525.xSearch in Google Scholar

[12] Shapiro L.B., On spaces coabsolute to a generalized Cantor discontinuum, Soviet Math. Dokl., 1986, 33, 870–874 Search in Google Scholar

[13] Shapiro L.B., On spaces coabsolute to dyadic compacta, Soviet Math. Dokl., 1987, 35, 434–438 Search in Google Scholar

[14] Turek S., Minimal dynamical systems for !-bounded groups, Acta Univ. Carolin. Math. Phys., 1994, 35(2), 77–81 Search in Google Scholar

[15] Turek S., Minimal actions on Cantor cubes, Bull. Polish Acad. Sci. Math., 2003, 51(2), 129–138 Search in Google Scholar

Published Online: 2013-10-30
Published in Print: 2014-1-1

© 2014 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 18.4.2024 from https://www.degruyter.com/document/doi/10.2478/s11533-013-0325-6/html
Scroll to top button