Article

Full entry | PDF   (0.1 MB)
Keywords:
Dugundji space; projective Boolean algebra; profinite lattice; supercompact
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.
References:
[B] Bell M.G.: Not all dyadic spaces are supercompact. Comment. Math. Univ. Carolinae 31 (1990), 775-779. MR 1091375 | Zbl 0716.54017
[BG] Bell M.G., Ginsburg J.: Compact spaces and spaces of maximal complete subgraphs. Trans. Amer. Math. Soc. 283 (1984), 329-338. MR 0735426 | Zbl 0554.54009
[CP] Clifford A.H., Preston B.: The algebraic theory of semigroups. vol. 1, Providence, 1964. Zbl 0238.20076
[Ha] Haydon R.: On a problem of Pelczynski: Miljutin spaces, Dugundji spaces and \${AE}(0\$-\$\dim)\$. Studia Math. 52 (1974), 23-31. MR 0418025
[He] Heindorf L.: Boolean semigroup rings and exponentials of compact, zero-dimensional spaces. Fund. Math. 135 (1990), 37-47. MR 1074647 | Zbl 0716.54006
[K] Koppelberg S.: Projective Boolean Algebras. Chapter 20 of: J.D. Monk (ed.), Handbook of Boolean algebras, Amsterdam, 1989, vol. 3, 741-773. MR 0991609 | Zbl 0258.06010
[N] Numakura K.: Theorems on compact totally disconnected semigroups and lattices. Proc. Amer. Math. Soc. 8 (1957), 623-626. MR 0087032 | Zbl 0081.25602
[S] Sčepin E.V.: Functors and uncountable powers of compacts (in Russian). Uspehi Mat. Nauk 36 (1981), 3-62. MR 0622720

Partner of