Zero-dimensional Dugundji spaces admit profinite lattice structures

Lutz Heindorf

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 329-334
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Heindorf, Lutz. "Zero-dimensional Dugundji spaces admit profinite lattice structures." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 329-334. <http://eudml.org/doc/247353>.

@article{Heindorf1992,
abstract = {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.},
author = {Heindorf, Lutz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Dugundji space; projective Boolean algebra; profinite lattice; supercompact; Dugundji space; projective Boolean algebra; profinite lattice; supercompact spaces},
language = {eng},
number = {2},
pages = {329-334},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Zero-dimensional Dugundji spaces admit profinite lattice structures},
url = {http://eudml.org/doc/247353},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Heindorf, Lutz
TI - Zero-dimensional Dugundji spaces admit profinite lattice structures
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 329
EP - 334
AB - 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.
LA - eng
KW - Dugundji space; projective Boolean algebra; profinite lattice; supercompact; Dugundji space; projective Boolean algebra; profinite lattice; supercompact spaces
UR - http://eudml.org/doc/247353
ER -

References

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  1. Bell M.G., Not all dyadic spaces are supercompact, Comment. Math. Univ. Carolinae 31 (1990), 775-779. (1990) Zbl0716.54017MR1091375
  2. Bell M.G., Ginsburg J., Compact spaces and spaces of maximal complete subgraphs, Trans. Amer. Math. Soc. 283 (1984), 329-338. (1984) Zbl0554.54009MR0735426
  3. Clifford A.H., Preston B., The algebraic theory of semigroups, vol. 1, Providence, 1964. Zbl0238.20076
  4. Haydon R., On a problem of Pelczynski: Miljutin spaces, Dugundji spaces and A E ( 0 - dim ) , Studia Math. 52 (1974), 23-31. (1974) MR0418025
  5. Heindorf L., Boolean semigroup rings and exponentials of compact, zero-dimensional spaces, Fund. Math. 135 (1990), 37-47. (1990) Zbl0716.54006MR1074647
  6. Koppelberg S., Projective Boolean Algebras, Chapter 20 of: J.D. Monk (ed.), Handbook of Boolean algebras, Amsterdam, 1989, vol. 3, 741-773. Zbl0258.06010MR0991609
  7. Numakura K., Theorems on compact totally disconnected semigroups and lattices, Proc. Amer. Math. Soc. 8 (1957), 623-626. (1957) Zbl0081.25602MR0087032
  8. Sčepin E.V., Functors and uncountable powers of compacts (in Russian), Uspehi Mat. Nauk 36 (1981), 3-62. (1981) MR0622720

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