54A05-GenericPoint.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{GenericPoint}
\pmcreated{2013-03-22 16:22:28}
\pmmodified{2013-03-22 16:22:28}
\pmowner{jocaps}{12118}
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\pmtitle{generic point}
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\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{54A05}
%\pmkeywords{generization}
%\pmkeywords{specialization}
%\pmkeywords{generic points}
\pmdefines{generic point}
\pmdefines{generic}

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