On homeomorphism groups of Menger continua-Reference-Cited by-同舟云学术

On homeomorphism groups of Menger continua

Published:2005-03-01 Issue:7 Volume:357 Page:2665-2679
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Dijkstra Jan

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2005-357-07/S0002-9947-05-03863-8/S0002-9947-05-03863-8.pdf

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4. Characterizing 𝑘-dimensional universal Menger compacta;Bestvina, Mladen;Mem. Amer. Math. Soc.,1988

5. On the dimensions of certain spaces of homeomorphisms;Brechner, Beverly L.;Trans. Amer. Math. Soc.,1966

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