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

• Critical point (a.k.a. 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

• 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

• 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 (x_n)_n ∈ N for which there are, for every neighbourhood V of x, infinitely many natural numbers n such that x_n ∈ V