generic point

Let $X$ be a topological space and suppose that $x\in X$. If for all $y\in X\backslash \{x\}$ we have $x\notin \overline{\{y\}}$ then we say that $x$ is a generic point. Equivalently, $x$ is generic iff it is not a specialization point of any point in $X$, other than $x$ itself.

Title	generic point
Canonical name	GenericPoint
Date of creation	2013-03-22 16:22:28
Last modified on	2013-03-22 16:22:28
Owner	jocaps (12118)
Last modified by	jocaps (12118)
Numerical id	8
Author	jocaps (12118)
Entry type	Definition
Classification	msc 54A05
Defines	generic point
Defines	generic