| Title:
|
Another note on countable Boolean algebras (English) |
| Author:
|
Heindorf, Lutz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
815-819 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation. (English) |
| Keyword:
|
Boolean algebra |
| Keyword:
|
subalgebra lattice |
| Keyword:
|
metrizability |
| MSC:
|
06E05 |
| MSC:
|
54E35 |
| MSC:
|
54H12 |
| idZBL:
|
Zbl 0887.06007 |
| idMR:
|
MR1440712 |
| . |
| Date available:
|
2009-01-08T18:28:11Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118889 |
| . |
| Reference:
|
[1] Bonnet R.: Subalgebras.Chapter 10 in vol. 2 of: J. D. Monk (ed.) {Handbook of Boolean algebras}, North-Holland, Amsterdam, 1989. MR 0991598 |
| Reference:
|
[2] Engelking R.: General Topology.PWN, Warsaw, 1977. Zbl 0684.54001, MR 0500780 |
| Reference:
|
[3] Gruenhage G.: Covering properties on $X^2\setminus \Delta$, W-sets, and compact subsets of $\Sigma$-products.Topology and its Applications 17 (1978), 287-304. MR 0752278 |
| Reference:
|
[4] Jech T.: A note on countable Boolean algebras.Algebra Universalis 14 (1982), 257-262. Zbl 0488.06007, MR 0635004 |
| Reference:
|
[5] Koppelberg S.: General theory of Boolean algebras.vol 1. of: J. D. Monk (ed.) {Handbook of Boolean algebras}, North-Holland, Amsterdam, 1989. MR 0991565 |
| Reference:
|
[6] Remmel J.B.: Complementation in the lattice of subalgebras of a Boolean algebra.Algebra Universalis 10 (1980), 48-64. Zbl 0432.06010, MR 0552156 |
| . |
