Compactifications and universal spaces

in extension theory

Author:
Alex Chigogidze

Journal:
Proc. Amer. Math. Soc. **128** (2000), 2187-2190

MSC (1991):
Primary 55M10; Secondary 54F45

DOI:
https://doi.org/10.1090/S0002-9939-99-05238-7

Published electronically:
October 29, 1999

MathSciNet review:
1653445

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

- iff for any space .
- There exists a -invertible map of a metrizable compactum with onto the Hilbert cube.

**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**

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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:
https://doi.org/10.1090/S0002-9939-99-05238-7

Keywords:
Compactification,
universal space,
cohomological dimension

Received by editor(s):
April 14, 1998

Received by editor(s) in revised form:
August 25, 1998

Published electronically:
October 29, 1999

Additional Notes:
The author was partially supported by NSERC research grant.

Communicated by:
Alan Dow

Article copyright:
© Copyright 2000
American Mathematical Society