Jeremy
Brazas
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My research interests include algebraic and
general topology. More specifically, my
interests deal with generalized theories of covering spaces,
topological algebra, and understanding homotopy groups of locally
complicated spaces.
Research Papers:
 J. Brazas, Generalized
covering space theories, Theory and Appl.
of Categories 30 (2015) 11321162.
pdf
 J. Brazas, P. Fabel, On fundamental
groups with the quotient topology, J.
Homotopy and Related Structures
10 (2015) 7191. arXiv
 J. Brazas, P. Fabel, Strongly
pseudoradial spaces, Topology
Proc. 46 (2015) 255276. arXiv
 J. Brazas, P. Fabel, Thick
Spanier
groups and the first shape group, Rocky Mountain J. Math. 44
(2014) 14151444. arXiv
 J. Brazas, Open
subgroups
of free topological groups, Fundamenta
Mathematicae 226 (2014) 1740. arXiv
 J. Brazas, Semicoverings,
coverings, overlays and open subgroups of the quasitopological
fundamental group, Topology Proc. 44 (2014) 285313.
 J. Brazas, The
fundamental group
as a topological group, Topology
Appl. 160 (2013) 170188. arXiv
 J. Brazas, Semicoverings:
a
generalization of covering space theory,
Homology Homotopy Appl.
14
(2012) 3363. pdf
 J. Brazas, The
topological
fundamental group and free topological
groups, Topology Appl. 158
(2011) 779802. arXiv
Math Education Papers:
 T. Abel, J. Brazas, Pedagogically
Inconvenient Functions for Teaching Transformations, College
Mathematics Journal, To Appear. 2016.
 J. Brazas, D. Priest, Using
the floor function to prove the countability of the rationals, AMATYC
Review 29 no. 2, 2008.
Selected Conference Talks:
 A characterization of the
unique path lifting property for the whisker topology, Joint
Meeting of the German and Polish Mathematical Societies (DMVPTM),
Invited talk in Wild Algebraic & Geometric Topology session,
Poznan, Poland, September 18, 2014. Slides
 Topological fundamental
groups and open subgroup theorems, Lloyd Roeling Lafayette
Mathematics Conference, Invited talk, UL Lafayette, November 9, 2013.
 Quasitopological
fundamental groups and the first shape map, 28th Summer
Conference on Topology and Its Applications, Invited talk in Continuum
Theory Session, Nippissing University, July 26, 2013. Abstract
Slides
 Open subgroups of free
topological groups, 47th
Spring Topology and Dynamics Conference, Central Connecticut State
University, March 24, 2013. Abstract
Slides
 Developing Digital
Literacy in the Calculus Sequence (Joint with Todd Abel), 28th
International Conference on Technology in Collegiate Teaching, Atlanta,
GA. March 12, 2016.
Ph.D.
Dissertation:
 J. Brazas, Homotopy
Mapping
Spaces, University of New
Hampshire Ph.D. Dissertation, 2011.
Miscellaneous
notes:
