Generalized-designs

Abstract

The generalization of designs can be considered as infinite designs. A finite set can be a part of an infinite set, a well-ordered set, a partial ordered set, or even a (discrete) topological space; in this paper designs are generalized due to this point of view. In this way for a mathematical structure ${\mathcal M}$, ${\mathcal M}$-designs are developed, especially some results in poset-designs are obtained.