Yes, three points define a plane. So any three points lie in some specific plane and are therefore co-planar.
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No, they always are From Wikipedia.org, "The World's Encyclopedia" when I searched coplanar In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three distinct points are always coplanar; but four points in space are usually not coplanar. Since 3 points are always coplanar. A point and line are always coplanar
Coplanar forces are a set of forces all of which act in the same plane. Non-coplanar forces are a set of forces in which at least one act in a direction incline to the plane formed by two of the forces.
The solution set is all points on the circle.
Take the set of points 1/n for all integers n. This is an isolated set of points- that is, for any of them there is an open ball about the point not containing any other point. However, this set has a limit point which is not contained in the set (namely 0), hence it is not closed.
A line segment is a set of points between the two main end points. A line segment is always connected and has no open spaces.