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1994 | 145 | 1 | 1-13
Tytuł artykułu

On absolute retracts of ω*

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $ω_1$ 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 ${0,1}^{ω_1}$.
Słowa kluczowe
Rocznik
Tom
145
Numer
1
Strony
1-13
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-11-04
poprawiono
1993-06-16
poprawiono
1993-10-27
Twórcy
autor
  • Dipartimento di Matematica, Università di Messina, 98186 Sant'Agata, Italy
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
  • Mathematics Department, Slippery Rock University, Slippery Rock, Pennsylvania 16057-1326, U.S.A.
Bibliografia
  • [1] B. Balcar and F. Franek, Independent families in complete Boolean algebras, Trans. Amer. Math. Soc. 274 (2) (1982), 607-617.
  • [2] W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer, 1974.
  • [3] R. Engelking, General Topology, Polish Scientific Publishers, Warszawa, 1977.
  • [4] A. M. Gleason, Projective topological spaces, Illinois Math. J. 2 (1958), 482-489.
  • [5] R. Haydon, On a problem of Pełczyński: Milutin spaces, Dugundji spaces and AE(0-dim), Studia Math. 52 (1974), 23-31.
  • [6] D. Maharam, Finitely additive measures on the integers, Sankhyā Ser. A 38 (1976), 44-59.
  • [7] J. Mioduszewski and L. Rudolf, H-closed and extremally disconnected Hausdorff spaces, Dissertationes Math. 66 (1969).
  • [8] J. R. Porter and R. G. Woods, Extensions and Absolutes of Hausdorff Spaces, Springer, 1988.
  • [9] L. Šapiro [L. Shapiro], A counterexample in the theory of dyadic compact spaces, Uspekhi Mat. Nauk 40 (5) (1985), 267-268 (in Russian).
  • [10] L. Šapiro [L. Shapiro], On spaces coabsolute to a generalized Cantor discontinuum, Soviet Math. Dokl. 33 (1986), 870-873.
  • [11] E. V. Ščepin [E. V. Shchepin], Topology of limits of uncountable inverse spectra, Russian Math. Surveys 31 (1976), 155-191.
  • [12] P. Simon, A closed separable subspace of βN which is not a retract, Trans. Amer. Math. Soc. 299 (1987), 641-655.
  • [13] A. Szymański, Some applications of tiny sequences, Rend. Circ. Mat. Palermo (2) Suppl. 3 (1984), 321-328.
  • [14] M. Talagrand, Non existence de relèvement pour certaines mesures finiement additives et rétractes de βℕ, Math. Ann. 256 (1981), 63-66.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv145i1p1bwm
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