Another note on countable Boolean algebras

Lutz Heindorf

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 4, page 815-819
  • ISSN: 0010-2628

Abstract

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We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.

How to cite

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Heindorf, Lutz. "Another note on countable Boolean algebras." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 815-819. <http://eudml.org/doc/247878>.

@article{Heindorf1996,
abstract = {We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.},
author = {Heindorf, Lutz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Boolean algebra; subalgebra lattice; metrizability; countable Boolean algebra; complement; metrizable space; compact zero-dimensional space; subalgebra lattice},
language = {eng},
number = {4},
pages = {815-819},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Another note on countable Boolean algebras},
url = {http://eudml.org/doc/247878},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Heindorf, Lutz
TI - Another note on countable Boolean algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 4
SP - 815
EP - 819
AB - We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.
LA - eng
KW - Boolean algebra; subalgebra lattice; metrizability; countable Boolean algebra; complement; metrizable space; compact zero-dimensional space; subalgebra lattice
UR - http://eudml.org/doc/247878
ER -

References

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  1. Bonnet R., Subalgebras, Chapter 10 in vol. 2 of: J. D. Monk (ed.) {Handbook of Boolean algebras}, North-Holland, Amsterdam, 1989. MR0991598
  2. Engelking R., General Topology, PWN, Warsaw, 1977. Zbl0684.54001MR0500780
  3. Gruenhage G., Covering properties on X 2 ∖ Δ , W-sets, and compact subsets of Σ -products, Topology and its Applications 17 (1978), 287-304. (1978) MR0752278
  4. Jech T., A note on countable Boolean algebras, Algebra Universalis 14 (1982), 257-262. (1982) Zbl0488.06007MR0635004
  5. Koppelberg S., General theory of Boolean algebras, vol 1. of: J. D. Monk (ed.) {Handbook of Boolean algebras}, North-Holland, Amsterdam, 1989. MR0991565
  6. Remmel J.B., Complementation in the lattice of subalgebras of a Boolean algebra, Algebra Universalis 10 (1980), 48-64. (1980) Zbl0432.06010MR0552156

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