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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local contractibility, cell-like maps, and dimension


Author: Jan van Mill
Journal: Proc. Amer. Math. Soc. 98 (1986), 534-536
MSC: Primary 55M10; Secondary 54C35
MathSciNet review: 857957
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Abstract: We consider the existence of cell-like maps $ f:$: $ {I^n} \to X$ such that no nonempty open subset of $ X$ is contractible in $ X$. From the Taylor Example, it is easy to construct such a map for $ n = \infty $. We show that there exists such a map for some finite $ n$ if (and only if) there exists a dimension raising cell-like map of a compactum.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857957-7
PII: S 0002-9939(1986)0857957-7
Keywords: Cell-like map, dimension, local contractibility
Article copyright: © Copyright 1986 American Mathematical Society