# Understanding connected point sets.

Prove whether the following is true or false. If it is false give a counter example.

If F is a collection, each element of which is a connected point set and each point set in F contains a limit point of every other point set in F, then UF is connected.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/discrete-math/understanding-connected-point-sets-34s#### Solution Preview

... generality, assume it lies entirely within C. Now D must be non-empty, so there must be an F_beta in F such that F_beta intersect D is non-empty. Since F_beta is connected, it must lie entirely within D. If a set is connected, it's ...