Geodesic
On van Douwen spaces and retracts of $\beta {\mathbb{N}}$
Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 345-368

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MR Zbl
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).
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).
DOI : 10.21136/MB.2007.133962
Classification : 54A25, 54A35, 54C15, 54D35
Keywords: $\beta \mathbb{N}$; retracts; two to one map; Stone-Čech compactification 
Dow, Alan. On van Douwen spaces and retracts of $\beta {\mathbb{N}}$. Mathematica Bohemica, Tome 132 (2007) no. 4, pp. 345-368. doi: 10.21136/MB.2007.133962
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