High Quality Content by WIKIPEDIA articles! In mathematics, in the fields general topology and particularly of algebraic geometry, a generic point P of a topological space X is an algebraic way of capturing the notion of a generic property: a generic property is a property of the generic point. Formally, a generic point is a point P such that every point Q of X is a specialization of P, in the sense of the specialization order (or preorder): the closure of P is the entire set: it is dense. This concept is only non-trivial for spaces that are not Hausdorff spaces, because a Hausdorff space with a generic point P can only be the singleton set {P}. The terminology arises from the case of the Zariski topology of algebraic varieties. For example having a generic point is a criterion to be an irreducible set.

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