# Compactness and Connectedness of sets

Can we check Compactness/Connectedness of sets in $R^{2}$ using some mathematica code ?

If Yes , Can anyone tell how ?

• How are the sets going to be specified? Mathematica has some functions such as CylindricalDecomposition that might help you, but they work primarily with inequalities in terms of $x$ and $y$. – Michael Seifert Apr 13 '16 at 14:37
• This question is very general and the answer is "of course, we can", if you are interested in a certain topological technique related to the general problem see e.g. this anser Finding minimal distance between two surfaces – Artes Apr 13 '16 at 15:17
• Can you give a specify example to compute – M.R. Apr 13 '16 at 19:23