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.
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.
Read more about this topic: Generic Point
Famous quotes containing the words definition and/or motivation:
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“Self-determination has to mean that the leader is your individual gut, and heart, and mind or we’re talking about power, again, and its rather well-known impurities. Who is really going to care whether you live or die and who is going to know the most intimate motivation for your laughter and your tears is the only person to be trusted to speak for you and to decide what you will or will not do.”
—June Jordan (b. 1939)