The discussion centers on proving that the union of two disjoint sets is disconnected, specifically addressing both open and closed sets. It is established that open disjoint sets inherently satisfy the definition of disconnectedness. The challenge lies in demonstrating the same for closed sets and cases involving one open and one closed set. Diagrams were utilized to visualize the concepts, reinforcing the conclusion that these sets remain disconnected.
PREREQUISITESMathematics students, particularly those studying topology and set theory, as well as educators seeking to clarify concepts of disconnectedness in sets.
jessicaw said:Homework Statement
union of 2 disjoint sets is disconnected
Homework Equations
The Attempt at a Solution
For open disjoint sets it is obvious as it is the definition of disconectedness.
So it remains to prove the closed sets/one open and open closed set case.
In any case, i draw some diagrams and i believe they are disconnected.