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Homeomorphism Groups of Homogeneous Spaces


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Title: Homeomorphism Groups of Homogeneous Spaces
Authors: Karube, Takashi
Issue Date: 28-Feb-1982
Publisher: 長崎大学教育学部
Citation: 長崎大学教育学部自然科学研究報告. vol.33, p.5-9; 1982
Abstract: Let X be a separable metrizable coset-space of a locally compact group, which has a local cross-section and admits a nontrivial flow. Let ℋ(X) be the group of homeomorphisms on X, endowed with the compact-open topology, and ℋ(X, x) the subspace of ℋ(X) consisting of those homeomorphisms which fix a point x of X. Then ℋ(X) is an l2-manifold if and only if X is an ANR and ℋ(X, x) is an l2-manifold. Among applications of this, we see that if X is the plane R2, or punctured real projective plane, or punctured torus, then ℋ(X) is an l2-manifold.
URI: http://hdl.handle.net/10069/32581
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 33

Citable URI : http://hdl.handle.net/10069/32581

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