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Universal absolute extensors in extension theory


Authors: Alex Karasev and Vesko Valov
Journal: Proc. Amer. Math. Soc. 134 (2006), 2473-2478
MSC (2000): Primary 55M10; Secondary 54F45
DOI: https://doi.org/10.1090/S0002-9939-06-08304-3
Published electronically: February 8, 2006
MathSciNet review: 2213722
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Abstract: Let $ L$ be a countable and locally finite CW complex. Suppose that the class of all metrizable compacta of extension dimension $ \le [L]$ contains a universal element which is an absolute extensor in dimension $ [L]$. Our main result shows that $ L$ is quasi-finite.


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Additional Information

Alex Karasev
Affiliation: Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, Ontario, Canada P1B 8L7
Email: alexandk@nipissingu.ca

Vesko Valov
Affiliation: Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, Ontario, Canada P1B 8L7
Email: veskov@nipissingu.ca

DOI: https://doi.org/10.1090/S0002-9939-06-08304-3
Keywords: Absolute extensors, universal compacta, extension dimension, cohomological dimension, quasi-finite complexes
Received by editor(s): June 8, 2004
Received by editor(s) in revised form: March 14, 2005
Published electronically: February 8, 2006
Additional Notes: The authors were partially supported by their NSERC grants.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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