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generic point
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.
== Definition and motivation ==
A generic point of the topological space ''X'' is a point ''P'' whose closure is all of ''X'', that is, a point that is dense in ''X''.〔David Mumford, The Red Book of Varieties and Schemes, Springer 1999〕
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.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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