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\noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
Banach J. Math. Anal. 8 (2014), no. 2, 67--78\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\footnotesize
\textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach
\textbf{\large{J}}ournal of \textbf{\large{M}}athematical
\textbf{\large{A}}nalysis}}\\
ISSN: 1735-8787 (electronic)\\
\textcolor[rgb]{0.00,0.00,0.84}{\textbf{www.emis.de/journals/BJMA/ }}\\
$\frac{{}}{\rule{4.55in}{0.05in}}$}\\[.5in]}

\title[The $CSCP$ and monolithic compacta]{The controlled separable complementation property and monolithic compacta}

\author[J. Ferrer]{Jes\'us Ferrer}

\address{ Department of Mathematical Analysis, University of Valencia, Dr. Moliner 50, Burjassot 46100, Spain.}
\email{\textcolor[rgb]{0.00,0.00,0.84}{Jesus.Ferrer@uv.es}}

\dedicatory{{\rm Communicated by J. E. Ball}}

\subjclass[2010]{Primary 46B10; Secondary 46B26.}

\keywords{Controlled separable complementation property, monolithic compacta, extensible space.}
\date{Received: May 10, 2013; Revised: Sep. 5, 2013; Accepted: Sep. 9, 2013.}

\begin{abstract}
For a compact $K$, a necessary condition for $C(K)$ to have the Controlled Separable Complementation Property is that $K$ be monolithic. In this paper, we prove that when $K$ contains no copy of $[0,\omega^\omega]$ and the set of points which admit a countable neighborhood base is a cofinite subset of $K$, then monolithicity of $K$ is sufficient for $C(K)$ to enjoy the Controlled Separable Complementation Property. We also show that, for this type of compacta $K$, the space $C(K)$ is separably extensible.\textbf{}
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