ON THE HOMEOMORPHISM GROUPS OF BRECHNER'S CONTINUA

In 1966 Brechner introduced a series of continua M with the property that their autohomeomorphism groups H(M) are totally disconnected but not zero-dimensional. In 2001 Brechner and Kawamura showed that these groups are almost zero-dimensional and thus one-dimensional by a theorem of Oversteegen and Tymchatyn. In the present note we show that the spaces H(M) are universal for the class of almost zero-dimensional spaces. We reach this result by constructing an imbedding of complete Erdos space into H(M). An interesting by-product of this imbedding is that it allows us to conclude that H(M) is not homeomorphic to complete Erdos space.