| Title:
|
Zero-dimensional Dugundji spaces admit profinite lattice structures (English) |
| Author:
|
Heindorf, Lutz |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
329-334 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras. (English) |
| Keyword:
|
Dugundji space |
| Keyword:
|
projective Boolean algebra |
| Keyword:
|
profinite lattice |
| Keyword:
|
supercompact |
| MSC:
|
06B35 |
| MSC:
|
06E05 |
| MSC:
|
54B25 |
| MSC:
|
54B35 |
| MSC:
|
54F50 |
| MSC:
|
54H12 |
| idZBL:
|
Zbl 0789.54011 |
| idMR:
|
MR1189664 |
| . |
| Date available:
|
2009-01-08T17:56:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118501 |
| . |
| Reference:
|
[B] Bell M.G.: Not all dyadic spaces are supercompact.Comment. Math. Univ. Carolinae 31 (1990), 775-779. Zbl 0716.54017, MR 1091375 |
| Reference:
|
[BG] Bell M.G., Ginsburg J.: Compact spaces and spaces of maximal complete subgraphs.Trans. Amer. Math. Soc. 283 (1984), 329-338. Zbl 0554.54009, MR 0735426 |
| Reference:
|
[CP] Clifford A.H., Preston B.: The algebraic theory of semigroups.vol. 1, Providence, 1964. Zbl 0238.20076 |
| Reference:
|
[Ha] Haydon R.: On a problem of Pelczynski: Miljutin spaces, Dugundji spaces and ${AE}(0$-$\dim)$.Studia Math. 52 (1974), 23-31. MR 0418025 |
| Reference:
|
[He] Heindorf L.: Boolean semigroup rings and exponentials of compact, zero-dimensional spaces.Fund. Math. 135 (1990), 37-47. Zbl 0716.54006, MR 1074647 |
| Reference:
|
[K] Koppelberg S.: Projective Boolean Algebras.Chapter 20 of: J.D. Monk (ed.), Handbook of Boolean algebras, Amsterdam, 1989, vol. 3, 741-773. Zbl 0258.06010, MR 0991609 |
| Reference:
|
[N] Numakura K.: Theorems on compact totally disconnected semigroups and lattices.Proc. Amer. Math. Soc. 8 (1957), 623-626. Zbl 0081.25602, MR 0087032 |
| Reference:
|
[S] Sčepin E.V.: Functors and uncountable powers of compacts (in Russian).Uspehi Mat. Nauk 36 (1981), 3-62. MR 0622720 |
| . |
