Subgroups of the Free Topological Group on [0, 1]

A Kurosh Subgroup Theorem for Topological Groups

“…We show, for example, that the free topological group F on a closed interval contains as a subgroup the free topological group on an open interval. This is a consequence of the general result that F contains copies of the free topological groups on each of its closed subspaces, a result which extends and generalizes our earlier work on the subgroups of F [15].…”

Characterization of Bases of Subgroups of Free Topological Groups

“…By Corollary 5, FM(X) contains FM (FM(X)). By Nickolas [12], FM(FM(X)) contains FM(FM(I)xFM(I)); and Theorem A implies that FM (FM (X) x FM (X)) contains FM(/4 t x A 2 ). As all of the above containments are closed, FM(X) has a closed subgroup topologically isomorphic to FM(/1 1 x A 2 ).…”

“…Proof of Theorem 1. It is shown in [12] that FM (A!") has a closed subgroup topologically isomorphic to FM (X x X).…”

Some Nonprojective Subgroups of Free Topological Groups

“…First we need a theorem of Nickolas [9] to the effect that In the abelian case we can obtain more complete results. of pointed simplicial sets, simplicial groups and simplicial abelian groups respectively.…”