Homeomorphism groups of manifolds and Erdös space

J.J. Dijkstra, J. van Mill

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Abstract

Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group H(M, D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification problem for H(M, D) as follows. If M is a one-dimensional topological manifold, then H(M, D) is homeomorphic to ℚ
Original languageEnglish
Pages (from-to)29-38 (electronic)
Number of pages10
JournalElectronic Research Announcements of the American Mathematical Society
Volume10
DOIs
Publication statusPublished - 2004

Bibliographical note

MR2048429

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