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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Examples of topological groups homeomorphic to $ l\sp f\sb 2$


Author: Tadeusz Dobrowolski
Journal: Proc. Amer. Math. Soc. 98 (1986), 303-311
MSC: Primary 57N20; Secondary 22A05, 54H15
MathSciNet review: 854038
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854038-3
PII: S 0002-9939(1986)0854038-3
Keywords: $ \sigma $-finite-dimensional metric groups, contractible groups, equiconnecting maps, measure preserving transformations, group spans, linearly independent arcs in linear spaces
Article copyright: © Copyright 1986 American Mathematical Society