Cohomological dimension

and metrizable spaces. II

Author:
Jerzy Dydak

Journal:
Trans. Amer. Math. Soc. **348** (1996), 1647-1661

MSC (1991):
Primary 55M11, 54F45

DOI:
https://doi.org/10.1090/S0002-9947-96-01536-X

MathSciNet review:
1333390

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Abstract | References | Similar Articles | Additional Information

Abstract: The main result of the first part of the paper is a generalization of the classical result of Menger-Urysohn : .

**Theorem.** *Suppose are subsets of a metrizable space and and are CW complexes. If is an absolute extensor for and is an absolute extensor for , then the join is an absolute extensor for . *

**Theorem.** *Suppose are subsets of a metrizable space. Then *

* for any ring with unity and *

* for any abelian group . *

**Theorem.** *Suppose is a sequence of CW complexes homotopy dominated by finite CW complexes. Then *

*a.**Given a separable, metrizable space such that , , there exists a metrizable compactification of such that , .**b.**There is a universal space of the class of all compact metrizable spaces such that for all .**c.**There is a completely metrizable and separable space such that for all with the property that any completely metrizable and separable space with for all embeds in as a closed subset.*

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Additional Information

**Jerzy Dydak**

Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996

Email:
dydak@math.utk.edu

DOI:
https://doi.org/10.1090/S0002-9947-96-01536-X

Keywords:
Dimension,
cohomological dimension,
Menger-Urysohn Theorem,
absolute extensors,
Eilenberg--Mac Lane spaces,
universal spaces,
compactifications

Received by editor(s):
December 11, 1992

Received by editor(s) in revised form:
May 3, 1995

Additional Notes:
Supported in part by a grant from the National Science Foundation

Article copyright:
© Copyright 1996
American Mathematical Society