## 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 language | English |
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Pages (from-to) | 29-38 (electronic) |

Number of pages | 10 |

Journal | Electronic Research Announcements of the American Mathematical Society |

Volume | 10 |

DOIs | |

Publication status | Published - 2004 |