<?xml version="1.0" encoding="UTF-8"?>

<record version="6" id="2121">
 <title>local base</title>
 <name>LocalBase</name>
 <created>2002-02-18 18:41:08</created>
 <modified>2007-03-26 04:00:11</modified>
 <type>Definition</type>
 <creator id="2760" name="yark"/>
 <author id="2760" name="yark"/>
 <author id="3" name="drini"/>
 <classification>
	<category scheme="msc" code="54-00"/>
 </classification>
 <synonyms>
	<synonym concept="local base" alias="base of a neighborhood system"/>
	<synonym concept="local base" alias="neighborhood base"/>
	<synonym concept="local base" alias="base of a neighbourhood system"/>
	<synonym concept="local base" alias="neighbourhood base"/>
 </synonyms>
 <related>
	<object name="FirstAxiomOfCountability"/>
	<object name="Neighborhood"/>
	<object name="NeighborhoodSystem"/>
 </related>
 <preamble></preamble>
 <content>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}.</content>
</record>
