A Critical Study on the Concept of Connected Set In Mathematics |

ABSTRACT:

A connected set is aset that cannot be partitioned into two non-empty subsets which are open in therelative topology induced on the set. Equivalently, it is a set which cannot bepartitioned into two nonempty subsets such thateach subset has no points in common with the set closure of theother. Let  be a topological space. A connected set in is a set which cannot be partitioned into two nonempty subsets which are open inthe relative topology induced on the set . Equivalently, it is a set which cannot be partitioned into twononempty subsets such that each subset has no points in common with the setclosure of the other. The space is a connected topological space if it is a connected subset of itself.