Examples of topological groups homeomorphic to 𝑙^{𝑓}₂

Dobrowolski, Tadeusz

doi:10.1090/S0002-9939-1986-0854038-3

Examples of topological groups homeomorphic to $l^ f_ 2$
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Proc. Amer. Math. Soc. 98 (1986), 303-311 Request permission

Abstract:

We prove that the following spaces are homeomorphic to $l_2^f$: (1) the group of piecewise continuous autotransformations of $[ - 1,1]$ preserving Lebesgue measure, and (2) certain subgroups obtained as group spans of linearly independent arcs in linear spaces. These are consequences of our discussion of the problem whether $\sigma$-fd-compact locally contractible metric groups must be either finite-dimensional or locally homeomorphic to $l_2^f$.

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