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Homogeneous and inhomogeneous manifolds. (English) Zbl 1151.54018

Les auteurs étudient les relations entre les propriétés de séparation, de recouvrement et d’homogénéité des variétés connexes. Ils montrent que toute variété homogène métalindelöf est séparée, et donnent une condition suffisante pour qu’une variété homogène dénombrablement paracompacte soit séparée. Ils montrent que, pour tout groupe dénombrable \(G\), il existe une variété de Lindelöf dont le groupe des homéomorphismes est isomorphe à \(G\).

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)
57R30 Foliations in differential topology; geometric theory
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