54-00-LocalBase.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{LocalBase}
\pmcreated{2013-03-22 12:22:16}
\pmmodified{2013-03-22 12:22:16}
\pmowner{yark}{2760}
\pmmodifier{yark}{2760}
\pmtitle{local base}
\pmrecord{9}{32121}
\pmprivacy{1}
\pmauthor{yark}{2760}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{54-00}
\pmsynonym{base of a neighborhood system}{LocalBase}
\pmsynonym{neighborhood base}{LocalBase}
\pmsynonym{base of a neighbourhood system}{LocalBase}
\pmsynonym{neighbourhood base}{LocalBase}
\pmrelated{FirstAxiomOfCountability}
\pmrelated{Neighborhood}
\pmrelated{NeighborhoodSystem}

\endmetadata


\begin{document}
Let $x$ be a point in a topological space $X$. A \emph{local base} around $x$, is a family of neighborhoods such that every neighborhood of $x$ contains a member of the family. A local base is also known as a \emph{neighborhood base}.
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\end{document}