Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Compactifications and universal spaces in extension theory

Author(s): Alex Chigogidze
Journal: Proc. Amer. Math. Soc. 128 (2000), 2187-2190.
MSC (1991): Primary 55M10; Secondary 54F45
Posted: October 29, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We show that for each countable simplicial complex $P$ the following conditions are equivalent:

  • $P \in AE(X)$ iff $P \in AE(\beta X)$ for any space $X$.
  • There exists a $P$-invertible map of a metrizable compactum $X$ with $P \in AE(X)$ onto the Hilbert cube.

References:

1.
A. Calder, J. Siegel, Homotopy and uniform homotopy, Trans. Amer. Math. Soc. 235 (1978), 245-270. MR 56:16619

2.
A. Chigogidze, Inverse Spectra, North Holland, Amsterdam, 1996. MR 97g:54001

3.
A. Chigogidze, Cohomological dimension of Tychonov spaces, Topology Appl. 79 (1997), 197-228. CMP 97:17

4.
A. Chigogidze, Infinite dimensional topology and Shape theory, in: Handbook of Geometric Topology, ed. by R. Daverman and R. Sher (to appear).

5.
A. N. Dranishnikov, Cohomological dimension is not preserved by Stone-\v{C}ech compactification, Comptes Rendus Bulgarian Acad. Sci. 41 (1988), 9-10. MR 90e:55002

6.
A. N. Dranishnikov, J. Dydak, Extension dimension and extension types, Proc. Steklov Math. Inst. 212 (1996), 55-88. CMP 98:16

7.
J. Dydak, Cohomological dimension of metrizable spaces. II, Trans. Amer. Math. Soc. 348 (1996), 1647-1661. MR 96h:55001

8.
J. Dydak, J. Mogilski, Universal cell-like maps, Proc. Amer. Math. Soc. 122 (1994), 943-948. MR 95a:55003

9.
J. Dydak, J. J. Walsh, Spaces without cohomological dimension preserving compactifications, Proc. Amer. Math. Soc. 113 (1991), 1155-1162. MR 92c:54039

10.
A. I. Karinski, On cohomological dimension of the Stone-\v{C}ech compactification, Vestnik Moscow Univ. no. 4 (1991), 8-11 (in Russian). MR 94a:55002

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 55M10, 54F45

Retrieve articles in all Journals with MSC (1991): 55M10, 54F45

Additional Information:

Alex Chigogidze
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6
Email: chigogid@math.usask.ca

DOI: 10.1090/S0002-9939-99-05238-7
PII: S 0002-9939(99)05238-7
Keywords: Compactification, universal space, cohomological dimension
Received by editor(s): April 14, 1998
Received by editor(s) in revised form: August 25, 1998
Posted: October 29, 1999
Additional Notes: The author was partially supported by NSERC research grant.
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google