Erdős space and homeomorphism groups of manifolds / Jan J. Dijkstra, Jan van Mill

Auteur: Dijkstra, Jan Jakobus (1953-) - AuteurCo-auteur: Mill, Jan van (1951-) - AuteurType de document: MonographieCollection: Memoirs of the American Mathematical Society ; 979Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, 2010Description: 1 vol. (V-62 p.) ; 26 cm ISBN: 9780821846353 ; br. ISSN: 0065-9266Résumé: 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. The authors present a complete solution to the topological classification problem for H(M,D) as follows. If M is a one-dimensional topological manifold, then they proved in an earlier paper that H(M,D) is homeomorphic to Qω, the countable power of the space of rational numbers. In all other cases they find in this paper that H(M,D) is homeomorphic to the famed Erdős space E, which consists of the vectors in Hilbert space ℓ2 with rational coordinates. They obtain the second result by developing topological characterizations of Erdős space. (Source : AMS).Bibliographie: Bibliogr. p. 61-62. Sujets MSC: 57S05 Manifolds and cell complexes -- Topological transformation groups -- Topological properties of groups of homeomorphisms or diffeomorphisms
57-02 Manifolds and cell complexes -- Research exposition (monographs, survey articles)
54F65 General topology -- Special properties -- Topological characterizations of particular spaces
Location Call Number Status Date Due
Couloir 04568-01 / Séries AMS (Browse Shelf) Available

Bibliogr. p. 61-62

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. The authors present a complete solution to the topological classification problem for H(M,D) as follows. If M is a one-dimensional topological manifold, then they proved in an earlier paper that H(M,D) is homeomorphic to Qω, the countable power of the space of rational numbers. In all other cases they find in this paper that H(M,D) is homeomorphic to the famed Erdős space E, which consists of the vectors in Hilbert space ℓ2 with rational coordinates. They obtain the second result by developing topological characterizations of Erdős space. (Source : AMS)

There are no comments for this item.

Log in to your account to post a comment.
Languages: English | Français | |