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

 

A metric condition which implies dimension $\leq 1$


Authors: Michael Levin and Roman Pol
Journal: Proc. Amer. Math. Soc. 125 (1997), 269-273
MSC (1991): Primary 54F45
MathSciNet review: 1389528
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Abstract: A class of $1$-dimensional spaces is distinguished by special type embeddings in compacta, or a corresponding metric property. In this setting, a simple proof of the Oversteegen-Tymchatyn theorem that the spaces of homeomorphisms of the Sierpi\'{n}ski's Carpet and the Menger Universal Curve have dimension $\leq 1$ is given.


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Additional Information

Michael Levin
Affiliation: Department of Mathematics, Haifa University, Mount Carmel, Haifa 31905, Israel
Email: levin@mathcs2.haifa.ac.il

Roman Pol
Affiliation: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
Email: pol@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03856-2
PII: S 0002-9939(97)03856-2
Received by editor(s): September 14, 1994
Communicated by: James E. West
Article copyright: © Copyright 1997 American Mathematical Society