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Carl
Eberhart's Research Interests in topology
A continuum is a
compact connected Hausdorf space. Continuum theory deals with
the construction and classification of continua. It provides a rich
field of investigation with an endless number of interesting questions
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Semigroups
of continuous mappings
A semigroup is a
set together with an associative binary operation. The set
of continuous selfmaps of a topological space forms a semigroup under composition.
I am interested in the interplay between the structure of such semigroups
and the structure of the underlying spaces.
A lattice is a partially
ordered set in which every two elements have a least upper bound and a
greatest lower bound. It turns out that lattices can be found
nearly everywhere in topology if one only looks for them. The
lattices provide a framework from which to ask interesting questions about
spaces.
Recent Papers
The Lattice of Knaster
Continua (with J.B. Fugate and Shannon Schumann), Proceedings
of the
First International
Conference on Continua, Puebla, Mexico,
Summer 2000
Open Mappings on
Knaster Continua (with J.B. Fugate and Shannon Schumann),
Fundamenta Mathematica,
162 (1999), pp 119-148.
Universal Maps on
Trees (with J.B. Fugate), Transactions
of the American Mathematical Society,
vol 350, no. 10, 1998,
pp 4235-4251. |