%%% This file is part of PlanetPhysics snapshot of 2011-09-01
%%% Primary Title: complex-valued continuous functions with compact support on H-lc
%%% Primary Category Code: 03.
%%% Filename: ComplexValuedContinuousFunctionsWithCompactSupportOnHLc.tex
%%% Version: 1
%%% Owner: bci1
%%% Author(s): bci1
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\begin{document}
\section{Class of complex-valued continuous functions with compact support on a
a locally compact Hausdorff space $H-{lc}$.}
\begin{definition}
Let $H_{lc}$ be a \htmladdnormallink{locally compact Hausdorff space}{http://planetphysics.us/encyclopedia/LocallyCompactHausdorffSpaces.html}. Then, one defines the notation \emph{$C_c (H_{lc})$} as the
space of complex-valued continuous \htmladdnormallink{functions}{http://planetphysics.us/encyclopedia/Bijective.html} with compact support on $H_{lc}$.
\end{definition}
{\bf Note:}
For simplicity, this is also denoted as $C_c(X)$ even though it is tacitly assumed that the \htmladdnormallink{topological}{http://planetphysics.us/encyclopedia/CoIntersections.html} space
$X = H_{lc}$.
\end{document}
