On homeomorphism groups of Menger continua
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- by Jan J. Dijkstra PDF
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Abstract:
It is shown that the homeomorphism groups of the (generalized) Sierpiński carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner’s proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdős space in the homeomorphism groups, is of independent interest.References
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Additional Information
- Jan J. Dijkstra
- Affiliation: Faculteit der Exacte Wetenschappen / Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
- MR Author ID: 58030
- Email: dijkstra@cs.vu.nl
- Received by editor(s): July 15, 2003
- Published electronically: March 1, 2005
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 357 (2005), 2665-2679
- MSC (2000): Primary 57S05
- DOI: https://doi.org/10.1090/S0002-9947-05-03863-8
- MathSciNet review: 2139522