# 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 (*x*_{n})_{n ∈ N}for which there are, for every neighbourhood*V*of*x*, infinitely many natural numbers*n*such that*x*∈_{n}*V*

- Accumulation point (or cluster point), a point

## See also

- Triangle center and Category:Triangle centers, special points associated with triangles
- Functor of points

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