MATHEMATICA BOHEMICA, Vol. 132, No. 4, pp. 345-368 (2007)

On van Douwen spaces and retracts of $\beta {\Bbb N}$

Alan Dow

Alan Dow, Department of Mathematics, UNC-Charlotte, 9201 University City Blvd., Charlotte, NC 28223-0001, e-mail: adow@uncc.edu, {\tt http://www.math.uncc.edu/ {}adow}

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

Keywords: $\beta \Bbb N$, retracts, two to one map, Stone-Cech compactification

Classification (MSC2000): 54A25, 54C15

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