List of mathematical properties of points

In mathematics, the following appear:


 * Algebraic point
 * Associated point
 * Base point
 * Closed point
 * Divisor point
 * Embedded point
 * Extreme point
 * Fermat point
 * Fixed point
 * Focal point
 * Geometric point
 * Hyperbolic equilibrium point
 * Ideal point
 * Inflection point
 * Integral point
 * Isolated point
 * Generic point
 * Heegner point
 * Lattice hole, Lattice point
 * Lebesgue point
 * Midpoint
 * Napoleon points
 * Non-singular point
 * Normal point
 * Parshin point
 * Periodic point
 * Pinch point
 * Point (geometry)
 * Point source
 * Rational point
 * Recurrent point
 * Regular point, Regular singular point
 * Saddle point
 * Semistable point
 * Separable point
 * Simple point
 * Singular point of a curve
 * Singular point of an algebraic variety
 * Smooth point
 * Special point
 * Stable point
 * Torsion point
 * Vertex (curve)
 * Weierstrass point

Calculus

 * 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

 * 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

 * 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
 * Accumulation point (or cluster point), a point x ∈ X of a sequence (xn)n ∈ N for which there are, for every neighbourhood V of x, infinitely many natural numbers n such that xn ∈ V