On van Douwen spaces and retracts of β

Alan S. Dow

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 4, page 345-368
  • ISSN: 0862-7959

Abstract

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Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of β . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of β expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).

How to cite

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Dow, Alan S.. "On van Douwen spaces and retracts of $\beta {\mathbb {N}}$." Mathematica Bohemica 132.4 (2007): 345-368. <http://eudml.org/doc/250251>.

@article{Dow2007,
abstract = {Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of $\beta \{\mathbb \{N\}\}$. We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of $\beta \{\mathbb \{N\}\}$ expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).},
author = {Dow, Alan S.},
journal = {Mathematica Bohemica},
keywords = {$\beta \mathbb \{N\}$; retracts; two to one map; Stone-Čech compactification; two to one map; Stone-Čech compactification},
language = {eng},
number = {4},
pages = {345-368},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On van Douwen spaces and retracts of $\beta \{\mathbb \{N\}\}$},
url = {http://eudml.org/doc/250251},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Dow, Alan S.
TI - On van Douwen spaces and retracts of $\beta {\mathbb {N}}$
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 4
SP - 345
EP - 368
AB - Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of $\beta {\mathbb {N}}$. We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of $\beta {\mathbb {N}}$ expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).
LA - eng
KW - $\beta \mathbb {N}$; retracts; two to one map; Stone-Čech compactification; two to one map; Stone-Čech compactification
UR - http://eudml.org/doc/250251
ER -

References

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  12. On spaces that are coabsolute with dyadic compacta, Dokl. Akad. Nauk SSSR 293 (1987), 1077–1081. (1987) MR0890202
  13. A closed separable subspace of β which is not a retract, Trans. Amer. Math. Soc. 299 (1987), 641–655. (1987) MR0869226
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  16. Two spaces homeomorphic to S e q ( p ) , Comment. Math. Univ. Carolin. 42 (2001), 209–218. (2001) MR1825385

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