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\begin{document}

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\section*{subsets of lctvs}

\hypertarget{lexicography_of_subsets_of_topological_vector_spaces}{}\section*{{Lexicography of Subsets of Topological Vector Spaces}}\label{lexicography_of_subsets_of_topological_vector_spaces}

\hypertarget{idea}{}\subsection*{{Idea}}\label{idea}

There are many different types of special subset of topological vector space. The purpose here is to list many of them, to note easy relationships between them, and to remark on their use.

\hypertarget{lexicography}{}\subsection*{{Lexicography}}\label{lexicography}

Some of these only make sense if the vector space is the dual of some other space.

\begin{itemize}%
\item Absorbing
\item Bounded
\item Bornivorous
\item Closed
\item Circled
\item Compact
\item Convex
\item Equicontinuous
\item Precompact
\item Radial
\item Weakly Compact
\item Weakly Bounded
\item Weakly Closed

\end{itemize}
[[!redirects Absorbing subset of a tvs]] [[!redirects absorbing subset of a tvs]] [[!redirects Absorbing subset of a lctvs]] [[!redirects absorbing subset of a lctvs]] [[!redirects Bounded subset of a tvs]] [[!redirects bounded subset of a tvs]] [[!redirects Bounded subset of a lctvs]] [[!redirects bounded subset of a lctvs]] [[!redirects Bornivorous subset of a tvs]] [[!redirects bornivorous subset of a tvs]] [[!redirects Bornivorous subset of a lctvs]] [[!redirects bornivorous subset of a lctvs]] [[!redirects Closed subset of a tvs]] [[!redirects closed subset of a tvs]] [[!redirects Closed subset of a lctvs]] [[!redirects closed subset of a lctvs]] [[!redirects Circled subset of a tvs]] [[!redirects circled subset of a tvs]] [[!redirects Circled subset of a lctvs]] [[!redirects circled subset of a lctvs]] [[!redirects Compact subset of a tvs]] [[!redirects compact subset of a tvs]] [[!redirects Compact subset of a lctvs]] [[!redirects compact subset of a lctvs]] [[!redirects Convex subset of a tvs]] [[!redirects convex subset of a tvs]] [[!redirects Convex subset of a lctvs]] [[!redirects convex subset of a lctvs]] [[!redirects equicontinuous]] [[!redirects Equicontinuous subset of a tvs]] [[!redirects equicontinuous subset of a tvs]] [[!redirects Equicontinuous subset of a lctvs]] [[!redirects equicontinuous subset of a lctvs]] [[!redirects Precompact subset of a tvs]] [[!redirects precompact subset of a tvs]] [[!redirects Precompact subset of a lctvs]] [[!redirects precompact subset of a lctvs]] [[!redirects Radial subset of a tvs]] [[!redirects radial subset of a tvs]] [[!redirects Radial subset of a lctvs]] [[!redirects radial subset of a lctvs]] [[!redirects Weakly Compact subset of a tvs]] [[!redirects weakly compact subset of a tvs]] [[!redirects Weakly Compact subset of a lctvs]] [[!redirects weakly compact subset of a lctvs]] [[!redirects Weakly Bounded subset of a tvs]] [[!redirects weakly bounded subset of a tvs]] [[!redirects Weakly Bounded subset of a lctvs]] [[!redirects weakly bounded subset of a lctvs]]



\end{document}