Some nonprojective subgroups of free topological groups

Brown, Ronald

doi:10.1090/S0002-9939-1975-0393326-7

Some nonprojective subgroups of free topological groups
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Proc. Amer. Math. Soc. 52 (1975), 433-440 Request permission

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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Subgroups of the free topological group on