%------------------------------------------------------------------------------ % Here please write the date of submission of paper or its revisions: %------------------------------------------------------------------------------ % \documentclass[12pt, reqno]{amsart} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} \textheight 22.5truecm \textwidth 14.5truecm \setlength{\oddsidemargin}{0.35in}\setlength{\evensidemargin}{0.35in} \setlength{\topmargin}{-.5cm} \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{summary}[theorem]{Summary} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{problem}[theorem]{Problem} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \numberwithin{equation}{section} \begin{document} \setcounter{page}{67} \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{} \end{abstract} \maketitle \vspace{4cm} \end{document} %------------------------------------------------------------------------------ % End of journal.tex %------------------------------------------------------------------------------ .