Sufficent Conditions for the preservation of Polygonal-Connectedness in an arbitrary normed space

In this article we prove that if X is a normed space and U is a polygonally-connected subset of X with M:=ᵢ:\ i∈ I\⊂ P( U), a non-empty arbitrary family of discrete, non-empty subsets of $ U, $ then the property of polygonal-connectedness is also preserved in the resulting set U( i∈ I Sᵢ), under appropriate conditions.