On absolute retracts of ω*

A. Bella; A. Błaszczyk; A. Szymański

Fundamenta Mathematicae (1994)

  • Volume: 145, Issue: 1, page 1-13
  • ISSN: 0016-2736

Abstract

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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 .

How to cite

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Bella, A., Błaszczyk, A., and Szymański, A.. "On absolute retracts of ω*." Fundamenta Mathematicae 145.1 (1994): 1-13. <http://eudml.org/doc/212032>.

@article{Bella1994,
abstract = {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 $\{0,1\}^\{ω_1\}$.},
author = {Bella, A., Błaszczyk, A., Szymański, A.},
journal = {Fundamenta Mathematicae},
keywords = {; absolute retracts; compact extremally disconnected spaces; continuum hypothesis; Gleason cover; continuous Gleason system},
language = {eng},
number = {1},
pages = {1-13},
title = {On absolute retracts of ω*},
url = {http://eudml.org/doc/212032},
volume = {145},
year = {1994},
}

TY - JOUR
AU - Bella, A.
AU - Błaszczyk, A.
AU - Szymański, A.
TI - On absolute retracts of ω*
JO - Fundamenta Mathematicae
PY - 1994
VL - 145
IS - 1
SP - 1
EP - 13
AB - 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 ${0,1}^{ω_1}$.
LA - eng
KW - ; absolute retracts; compact extremally disconnected spaces; continuum hypothesis; Gleason cover; continuous Gleason system
UR - http://eudml.org/doc/212032
ER -

References

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  12. [12] P. Simon, A closed separable subspace of βN which is not a retract, Trans. Amer. Math. Soc. 299 (1987), 641-655. Zbl0613.54004
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