21 citations · 86 across the 22 of their papers we have counts for
24 papers
Tree-like is not a transitive relation on paths
Jeremy Brazas, Gregory R. Conner, Paul Fabel +1
The notions of tree-like loop and Lipschitz tree-like loop were introduced by Hambly and Lyons in their 2010 Annals of Mathematics paper. They showed that the Lipschitz tree-like p…
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 zero dimensional sequential spaces
Paul Fabel
We develop tools to recognize sequential spaces with large inductive dimension zero. We show the Hawaiian earring group is 0 dimensional, when endowed with the quotient topolog…
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…
Strongly Pseudoradial Spaces
Jeremy Brazas, Paul Fabel
The "weakly Hausdorff" property for pseudoradial spaces fails to be naturally characterized by unique convergence of transfinite sequences. In response, we develop the category $\m…