A metric condition which implies dimension $\le 1$
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- by Michael Levin and Roman Pol PDF
- Proc. Amer. Math. Soc. 125 (1997), 269-273 Request permission
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 Sierpiński’s Carpet and the Menger Universal Curve have dimension $\leq 1$ is given.References
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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
- Received by editor(s): September 14, 1994
- Communicated by: James E. West
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 269-273
- MSC (1991): Primary 54F45
- DOI: https://doi.org/10.1090/S0002-9939-97-03856-2
- MathSciNet review: 1389528