On homeomorphism groups of Menger continua

Dijkstra, Jan

doi:10.1090/S0002-9947-05-03863-8

On homeomorphism groups of Menger continua
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by Jan J. Dijkstra PDF

Trans. Amer. Math. Soc. 357 (2005), 2665-2679 Request permission

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.

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