Carl Eberhart's Research Interests in topology
  • Theory of continua 
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 .
  • 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.
  • Lattices
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.