# boundary of any finite set of points in the plane

The problem is sketch "boundary of any finite set of points in the plane" and determine its boundary. I'm totally confused since there'are infinitely finite sets in the plane, such as one point alone. How can I sketch its picu

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Don't you mean convex envelope of the points instead of topological boundary? – Berci Sep 30 '12 at 11:34

@Frank: They are indeed part of the boundary. If $F$ is a finite set in the plane, its boundary is itself $F$. The problem is asking you simply to sketch some finite set and indicate its boundary; there are, as you say, infinitely many different pictures that you could correctly sketch. – Brian M. Scott Sep 30 '12 at 6:58