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