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 to which no answer is yet known. 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.