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.