Determining continuity of regions/curves from inequalities

*To*: mathgroup at smc.vnet.net*Subject*: [mg67216] Determining continuity of regions/curves from inequalities*From*: "Bonny Banerjee" <banerjee at cse.ohio-state.edu>*Date*: Tue, 13 Jun 2006 01:06:59 -0400 (EDT)*Organization*: Ohio State University*Sender*: owner-wri-mathgroup at wolfram.com

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.

**Follow-Ups**:**Re: Determining continuity of regions/curves from inequalities***From:*"Carl K. Woll" <carlw@wolfram.com>

**Re: Determining continuity of regions/curves from inequalities***From:*Daniel Lichtblau <danl@wolfram.com>

**Re: Determining continuity of regions/curves from inequalities***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>