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<record version="3" id="9367">
 <title>full subgroup</title>
 <name>FullSubgroup</name>
 <created>2007-05-12 10:51:14</created>
 <modified>2007-06-11 11:13:04</modified>
 <type>Definition</type>
 <creator id="13753" name="Mathprof"/>
 <author id="13753" name="Mathprof"/>
 <classification>
	<category scheme="msc" code="22A05"/>
 </classification>
 <synonyms>
	<synonym concept="full subgroup" alias="open subgroup"/>
	<synonym concept="full subgroup" alias="clopen subgroup"/>
 </synonyms>
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 <content>A subgroup of a topological group is \emph{full} if it has a nonempty interior.

Theorem. A full subgroup is both open and closed.

\begin{thebibliography}{99}
\bibitem{PRH} Paul R. Halmos, \emph{Measure Theory}, Springer-Verlag (1974).
\end{thebibliography}</content>
</record>
