21 citations · 86 across the 22 of their papers we have counts for
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The Hawaiian earring group is topologically incomplete
Paul Fabel
The premier exhibition of the following phenomenon: The fundamental group of any Peano continuum constructed in similar fashion to the Hawaiian earring admits two natural distinct…
A characterization of spaces with discrete topological fundamental group
Paul Fabel
We offer a counterexample to a theorem in the literature and then repair the theorem as follows: The fundamental group of a locally path connected metric space inherits the discret…
A retraction theorem for topological fundamental groups with application to the Hawaiian earring
Paul Fabel
A characterization of regular topological fundamental groups yields a `no retraction theorem' for spaces constructed in similar fashion to the Hawaiian earring.
Topological fundamental groups can distinguish spaces with isomorphic homotopy groups
Paul Fabel
We exhibit a map f between aspherical spaces X and Y such that f induces an isomorphism on homotopy groups but, with natural topologies, X and Y fail to have homeomorphic fundament…
A monomorphism theorem for the inverse limit of nested retracts
Paul Fabel
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the…
The fundamental group of the harmonic archipelago
Paul Fabel
The harmonic archipelago HA is obtained by attaching a large pinched annulus to every pair of consecutive loops of the Hawaiian earring. We clarify the fundamental group pi1(HA) as…