On van Douwen spaces and retracts of β ℕ

Alan S. Dow

Mathematica Bohemica (2007)

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

Abstract

top
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 ℕ . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of β ℕ expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).

How to cite

top

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

top
  1. 10.4064/fm-145-1-1-13, Fund. Math. 145 (1994), 1–13. (1994) MR1295157DOI10.4064/fm-145-1-1-13
  2. On minimal dynamical systems on Boolean algebras, Comment. Math. Univ. Carolin. 31 (1990), 7–11. (1990) MR1056164
  3. 10.1016/0166-8641(93)90145-4, Topology Appl. 51 (1993), 125–139. (1993) MR1229708DOI10.1016/0166-8641(93)90145-4
  4. Rigid Stone spaces within Z F C , Proc. Amer. Math. Soc. 102 (1988), 745–748. (1988) MR0929014
  5. β 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
  6. On n -to-one continuous images of β ℕ , Preprint 2005. MR2361681
  7. 10.1007/BFb0094103, Lecture Notes Math., vol. 1596, Springer, Berlin, 1994. With an appendix by Sakaé Fuchino. MR1329090DOI10.1007/BFb0094103
  8. Recent progress in the topological theory of semigroups and the algebra of β S , Recent progress in general topology, II, North-Holland, Amsterdam, 2002, pp. 227–251. (2002) MR1970000
  9. 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
  10. 10.1016/j.topol.2004.06.015, Topology Appl. 153 (2006), 2272–2277. (2006) Zbl1099.54016MR2238730DOI10.1016/j.topol.2004.06.015
  11. An Introduction to β ω , Handbook of Set-Theoretic Topology, K. Kunen, J. E. Vaughan (eds.), Elsevier Science Publishers BV, North-Holland, Amsterdam, 1984, pp. 503–567. (1984) MR0776630
  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 ℕ which is not a retract, Trans. Amer. Math. Soc. 299 (1987), 641–655. (1987) MR0869226
  14. 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
  15. 10.1007/BF01450944, Math. Ann. 256 (1981), 63–66. (1981) MR0620123DOI10.1007/BF01450944
  16. Two spaces homeomorphic to S e q ( p ) , Comment. Math. Univ. Carolin. 42 (2001), 209–218. (2001) MR1825385

NotesEmbed ?

top

You must be logged in to post comments.