A geometric figure is open if any part of the boundary of the figure is not part of the figure.  

The clearest example of this is a graph of inequalities. Figure 1 is the graph of a system of inequalities. The points on the line y < 3  x are not part of the boundary. Since the inequality y < 3  x does not include the points on the line, the shaded geometric figure is open.  

In figure 2, the inequality y <= 3  x does include the points on the line, so the shaded geometric figure is not open. 
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