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Hilbert subgroups of the Full Homeomorphism Group of a Topological Group


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Title: Hilbert subgroups of the Full Homeomorphism Group of a Topological Group
Other Titles: 位相群の全位相変換群のヒルベルト部分群
Authors: Karube, Takashi
Authors (alternative): 苅部, 孝
Issue Date: 28-Feb-1977
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.28, p.11-22; 1977
Abstract: Let ℋ be the full homeomorphism group (with the compact-open topology) of a finite-dimensional connected locally compact nontrivial topological group. Then we can actually construct in ℋ a closed subgroup intersecting each coset of the automorphism group at most one point. The subgroup is homeomorphic to the infinite-dimensional separable Hilbert space but is not complete with respect to the uniformity of compact convergence defined by the right uniformity of the base group. The similar results hold for the full homeomorphism group of a Hausdorff space that is locally Euclidean around at least one point.
URI: http://hdl.handle.net/10069/32781
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 28

Citable URI : http://hdl.handle.net/10069/32781

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