21 citations · 86 across the 22 of their papers we have counts for
9 papers · 1 filter
On R-trees, homotopies, and covering maps
Jeremy Brazas, Gregory R. Conner, Paul Fabel +1
A map has the \emph{unique path lifting} property if every path in , after a choice of an initial point, lifts uniquely to a path in . We prove that if a group …
A natural pseudometric on homotopy groups of metric spaces
Jeremy Brazas, Paul Fabel
For a path-connected metric space , the -th homotopy group inherits a natural pseudometric from the -th iterated loop space with the uniform metric. This pseu…
On fundamental groups with the quotient topology
Jeremy Brazas, Paul Fabel
The quasitopological fundamental group is the fundamental group endowed with the natural quotient topology inherited from the space of based loops and is typi…
Compactly generated quasitopological homotopy groups with discontinuous multiplication
Paul Fabel
For each positive integer Q there exists a path connected metric compactum X such that the Qth-homotopy group of X is compactly generated but not a topological group (with the quot…
Embedding planar compacta in planar continua with application: homotopic maps between planar Peano continua are characterized by the fundamental group homomorphism
Paul Fabel
A planar compactum with connected complement can be an embedded in a cellular continuum by attaching a null sequence of arcs. Two based maps f and g from a planar Peano continuum X…
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…