Coverable semigroups

Abstract

The concept of a semilattice having small semilattices has been studied and some equivalences of this property have been investigated. In the process of investigating semilattices, the author found a class of semigroups called coverable semigroups, and the interesting fact about it is that a necessary and sufficient condition for a compact semilattice to have small semilattices is to be coverable. Also by virtue of the concept of coverable semigroups, one can show that the usual interval is costable instead of the more intricate method of proving it by producing an arc.