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Determining continuity of regions/curves from inequalities
Is there an easy way in Mathematica to determine whether the region or curve formed by a system of inequalities is continuous or not? For example, the output of some function (e.g. Reduce) might be as follows: x>2 && y>0 which forms a continuous region. Again, the following output (x<2 && y<0) || (x>2 && y>0) is not continuous. Similarly, for curves. Given such a system of inequalities, how to determine whether the region/curve it forms is continuous or not? Or in other words, if I pick any two random points, say P1 and P2, lying on the output curve/region, does there exist a continuous path lying entirely within the output curve/region from P1 to P2? Any help will be appreciated. Thanks, Bonny.