List of mathematical properties of points

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In mathematics, the following appear:

Calculus[edit]

  • Critical point (aka stationary point), any value v in the domain of a differentiable function of any real or complex variable, such that the derivative of v is 0 or undefined

Geometry[edit]

  • Antipodal point, the point diametrically opposite to another point on a sphere, such that a line drawn between them passes through the centre of the sphere and forms a true diameter
  • Conjugate point, any point that can almost be joined to another by a 1-parameter family of geodesics (e.g., the antipodes of a sphere, which are linkable by any meridian
  • Vertex (geometry), a point that describes a corner or intersection of a geometric shape
    • Apex (geometry), the vertex that is in some sense the highest of the figure to which it belongs

Topology[edit]

  • Adherent point, a point x in topological space X such that every open set containing x contains at least one point of a subset A
  • Condensation point, any point p of a subset S of a topological space, such that every open neighbourhood of p contains uncountably many points of S
  • Limit point, a set S in a topological space X is a point x (which is in X, but not necessarily in S) that can be approximated by points of S, since every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself

See also[edit]