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Proceedings of the American Mathematical Society

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Some nonprojective subgroups of free topological groups


Author: Ronald Brown
Journal: Proc. Amer. Math. Soc. 52 (1975), 433-440
MSC: Primary 22A05
DOI: https://doi.org/10.1090/S0002-9939-1975-0393326-7
MathSciNet review: 0393326
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Abstract: For the free topological group on an interval $ [a,b]$ a family of closed, locally path-connected subgroups is given such that each group is not projective and so not free topological. Simplicial methods are used, and the test for nonprojectivity is nonfreeness of the group of path components. Similar results are given for the abelian case.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0393326-7
Keywords: Free topological group, projective topological group
Article copyright: © Copyright 1975 American Mathematical Society

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