Question about Connected point sets
Prove whether the following is true or false. If it is false give a counter example.
If M is a connected point set, the cl(M) is connected.© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/discrete-math/question-about-connected-point-sets-33g
...re C and D are disjoint, non-empty, open subsets of cl(M). Now M is connected and is a subset of cl(M). Therefore by "Lemma A", M must lie entirely within either C or D. Suppose M is a subset of C. Then cl(M) is a subset of cl(C). ...