21 citations · 86 across the 22 of their papers we have counts for
7 papers · 1 filter
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…
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…
On low dimensional KC-spaces
Paul Fabel
The KC property, a separation axiom between weakly Hausdorff and Hausdorff, requires compact subsets to be closed. Various assumptions involving local conditions, dimension, connec…
Multiplication is discontinuous in the Hawaiian earring group (with the quotient topology)
Paul Fabel
The natural quotient map q from the space of based loops in the Hawaiian earring onto the fundamental group provides a new example of a quotient map such that q x q fails to be a q…
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…
The topological Hawaiian earring group does not embed in the inverse limit of free groups
Paul Fabel
Endowed with natural topologies, the fundamental group of the Hawaiian earring continuously injects into the inverse limit of free groups. This note shows the injection fails to ha…