On homeomorphism groups of Menger continua

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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 Erdo″s space in the homeomorphism groups, is of independent interest. ©2005 American Mathematical Society.
Original languageEnglish
Pages (from-to)2665-2679 (electronic)
JournalTransactions of the American Mathematical Society
Volume357
Issue number7
DOIs
Publication statusPublished - 2005

Bibliographical note

MR2139522

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