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

Mathematica Bohemica (2007)

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

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topDow, 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

top- On absolute retracts of ${\omega}^{*}$, Fund. Math. 145 (1994), 1–13. (1994) MR1295157
- On minimal dynamical systems on Boolean algebras, Comment. Math. Univ. Carolin. 31 (1990), 7–11. (1990) MR1056164
- Applications of maximal topologies, Topology Appl. 51 (1993), 125–139. (1993) MR1229708
- Rigid Stone spaces within $\mathrm{Z}FC$, Proc. Amer. Math. Soc. 102 (1988), 745–748. (1988) MR0929014
- $\beta \mathbb{N}$, The work of Mary Ellen Rudin (Madison, WI, 1991), Ann. New York Acad. Sci., vol. 705, New York Acad. Sci., New York, 1993, pp. 47–66. (1993) MR1277880
- On $n$-to-one continuous images of $\beta \mathbb{N}$, Preprint 2005. MR2361681
- Nearly projective Boolean algebras, Lecture Notes Math., vol. 1596, Springer, Berlin, 1994. With an appendix by Sakaé Fuchino. MR1329090
- Recent progress in the topological theory of semigroups and the algebra of $\beta S$, Recent progress in general topology, II, North-Holland, Amsterdam, 2002, pp. 227–251. (2002) MR1970000
- Characterizations of Cohen algebras, Papers on General Topology and Applications (Madison, WI, 1991), Ann. New York Acad. Sci., vol. 704, New York Acad. Sci., New York, 1993, pp. 222–237. (1993) Zbl0830.06006MR1277859
- The weight of certain images of ${\omega}^{*}$, Topology Appl. 153 (2006), 2272–2277. (2006) Zbl1099.54016MR2238730
- An Introduction to $\beta \omega $, Handbook of Set-Theoretic Topology, K. Kunen, J. E. Vaughan (eds.), Elsevier Science Publishers BV, North-Holland, Amsterdam, 1984, pp. 503–567. (1984) MR0776630
- On spaces that are coabsolute with dyadic compacta, Dokl. Akad. Nauk SSSR 293 (1987), 1077–1081. (1987) MR0890202
- A closed separable subspace of $\beta \mathbb{N}$ which is not a retract, Trans. Amer. Math. Soc. 299 (1987), 641–655. (1987) MR0869226
- Some applications of tiny sequences, Proceedings of the 11th Winter School on Abstract Analysis (Železná Ruda, 1983), Suppl. 3, 1984, pp. 321–328. (1984) MR0744396
- Non existence de relèvement pour certaines mesures finiement additives et retractés de $\beta \mathbb{N}$, Math. Ann. 256 (1981), 63–66. (1981) MR0620123
- Two spaces homeomorphic to $\mathrm{S}eq\left(p\right)$, Comment. Math. Univ. Carolin. 42 (2001), 209–218. (2001) MR1825385

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