On absolute retracts of ω*
Bella, A. ; Błaszczyk, A. ; Szymański, A.
Fundamenta Mathematicae, Tome 144 (1994), p. 1-13 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight ω1 is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same π-weight), then X is homeomorphic to the Gleason space over the Cantor cube 0,1ω1.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:212032 
@article{bwmeta1.element.bwnjournal-article-fmv145i1p1bwm,
     author = {A. Bella and A. B\l aszczyk and A. Szyma\'nski},
     title = {On absolute retracts of $\omega$*},
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {1-13},
     zbl = {0834.54021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv145i1p1bwm}
}

Bella, A.; Błaszczyk, A.; Szymański, A. On absolute retracts of ω*. Fundamenta Mathematicae, Tome 144 (1994) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv145i1p1bwm/

[00000] [1] B. Balcar and F. Franek, Independent families in complete Boolean algebras, Trans. Amer. Math. Soc. 274 (2) (1982), 607-617. | Zbl 0527.06008

[00001] [2] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer, 1974.

[00002] [3] R. Engelking, General Topology, Polish Scientific Publishers, Warszawa, 1977.

[00003] [4] A. M. Gleason, Projective topological spaces, Illinois Math. J. 2 (1958), 482-489. | Zbl 0083.17401

[00004] [5] R. Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23-31. | Zbl 0294.46016

[00005] [6] D. Maharam, Finitely additive measures on the integers, Sankhyā Ser. A 38 (1976), 44-59. | Zbl 0383.60008

[00006] [7] J. Mioduszewski and L. Rudolf, H-closed and extremally disconnected Hausdorff spaces, Dissertationes Math. 66 (1969). | Zbl 0204.22404

[00007] [8] J. R. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer, 1988. | Zbl 0652.54016

[00008] [9] L. Šapiro [L. Shapiro], A counterexample in the theory of dyadic compact spaces, Uspekhi Mat. Nauk 40 (5) (1985), 267-268 (in Russian).

[00009] [10] L. Šapiro [L. Shapiro], On spaces coabsolute to a generalized Cantor discontinuum, Soviet Math. Dokl. 33 (1986), 870-873. | Zbl 0604.54027

[00010] [11] E. V. Ščepin [E. V. Shchepin], Topology of limits of uncountable inverse spectra, Russian Math. Surveys 31 (1976), 155-191. | Zbl 0356.54026

[00011] [12] P. Simon, A closed separable subspace of βN which is not a retract, Trans. Amer. Math. Soc. 299 (1987), 641-655. | Zbl 0613.54004

[00012] [13] A. Szymański, Some applications of tiny sequences, Rend. Circ. Mat. Palermo (2) Suppl. 3 (1984), 321-328. | Zbl 0549.54003

[00013] [14] M. Talagrand, Non existence de relèvement pour certaines mesures finiement additives et rétractes de βℕ, Math. Ann. 256 (1981), 63-66. | Zbl 0467.28004