CURVE IN NEIGHBOURHOOD OF POINT
Definition
An object is a <CURVE IN NEIGHBOURHOOD OF POINT> if and only if: it is a <CURVE>; it is that part of another curve in the neighbourhood a <METRIC SPACE POINT>. The properties, such as tangent and curvature, of a curve_in_neighbourhood_of_point are determined by shrinking the size of the neighbourhood until they become well defined. The neighbourhood can surround the specified point on the curve, or can be on one side only. The curve that has the <CURVE IN NEIGHBOURHOOD OF POINT> is given by a cCURVE WITHIN CURVE>. A <METRIC SPACE POINT> that is within the <CURVE IN NEIGHBOURHOOD OF POINT> is given by a <POINT WITHIN CURVE>