Boolean algebras admitting a countable minimally acting group

Aleksander Błaszczyk; Andrzej Kucharski; Sławomir Turek

Open Mathematics (2014)

  • Volume: 12, Issue: 1, page 46-56
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Aleksander Błaszczyk, Andrzej Kucharski, and Sławomir Turek. "Boolean algebras admitting a countable minimally acting group." Open Mathematics 12.1 (2014): 46-56. <http://eudml.org/doc/268974>.

@article{AleksanderBłaszczyk2014,
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.},
author = {Aleksander Błaszczyk, Andrzej Kucharski, Sławomir Turek},
journal = {Open Mathematics},
keywords = {Projective Boolean algebra; Dense subalgebra; Regular subalgebra; Cohen skeleton; Cohen algebra; Group of automorphisms; projective Boolean algebra; minimally acting group; dense subalgebra; countable chain condition},
language = {eng},
number = {1},
pages = {46-56},
title = {Boolean algebras admitting a countable minimally acting group},
url = {http://eudml.org/doc/268974},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Aleksander Błaszczyk
AU - Andrzej Kucharski
AU - Sławomir Turek
TI - Boolean algebras admitting a countable minimally acting group
JO - Open Mathematics
PY - 2014
VL - 12
IS - 1
SP - 46
EP - 56
AB - 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.
LA - eng
KW - Projective Boolean algebra; Dense subalgebra; Regular subalgebra; Cohen skeleton; Cohen algebra; Group of automorphisms; projective Boolean algebra; minimally acting group; dense subalgebra; countable chain condition
UR - http://eudml.org/doc/268974
ER -

References

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  8. [8] Heindorf L., Shapiro L.B., Nearly Projective Boolean Algebras, Lect. Notes Math., 1596, Springer, Berlin, 1994 
  9. [9] Koppelberg S., Handbook of Boolean Algebras, 1, North-Holland, Amsterdam, 1989 
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  11. [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 Zbl0830.06006
  12. [12] Shapiro L.B., On spaces coabsolute to a generalized Cantor discontinuum, Soviet Math. Dokl., 1986, 33, 870–874 Zbl0604.54027
  13. [13] Shapiro L.B., On spaces coabsolute to dyadic compacta, Soviet Math. Dokl., 1987, 35, 434–438 Zbl0641.54006
  14. [14] Turek S., Minimal dynamical systems for !-bounded groups, Acta Univ. Carolin. Math. Phys., 1994, 35(2), 77–81 Zbl0831.54035
  15. [15] Turek S., Minimal actions on Cantor cubes, Bull. Polish Acad. Sci. Math., 2003, 51(2), 129–138 Zbl1047.37005

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