Vol. 44, No. 1, 1973

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Topological groups whose underlying spaces are separable Fréchet manifolds

James Edgar Keesling

Vol. 44 (1973), No. 1, 181–189

Let G be a topological group and let G denote the space of all Lebesgue measurable functions from the unit interval [0,1] into G with the topology of convergence in measure. With this topology and with pointwise multiplication as the group operation, G is a topological group. If G is separable and has a complete metric and has more than one point, then Bessaga and Pefczyński have shown that G is homeomorphic to l2, separable infinite-dimensional Hilbert space. This fact is used in this paper to show the existence of separable Fréchet manifolds which are topological groups and which have certain algebraic and topological properties.

Mathematical Subject Classification 2000
Primary: 58B99
Secondary: 22A99
Received: 10 August 1971
Revised: 20 March 1972
Published: 1 January 1973
James Edgar Keesling