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\title[Template]{Template for the Proceedings of ICTAA 2018}

\author{Mart Abel}

\address{Institute of Mathematics and Natural Sciences, University of\break Tallinn, 25 Narva Str., Room A-416, 10120 Tallinn, ESTONIA}

\email{mart.abel@tlu.ee}

\thanks{I thank all persons who send their good papers for the publications.}

\keywords{Template file, topological algebras.}

\subjclass[2010]{Primary: 46H05; Secondary: 13J99, 22A05}

\begin{abstract}
Here we give the example of the paper style file for the Proceedings.
\end{abstract}

\maketitle



\section{Introduction}
Please follow the example given here for Your file for Proceedings. I will put as an example some results from the paper from the Proceedings of ICTAA 2013.
\begin{definition}
This is the {\bf template file}.
\end{definition}
\section{Results about compact and precompact elements}
We start with a generalization of Lemma 4.2 from \cite{2}, p. 724.\par\vskip .2cm
\begin{lemma} 
Let $A$ be a topological group $($in particular, a topological ring or a topological algebra$)$. Then the set $P(A)$ is closed in $L(A)$.
\end{lemma}
\begin{proof}
Let $T\in L(A)$ be an arbitrary map from the closure of $P(A)$ in the {\it topology of bounded convergence} in $L(A)$. Then there exist a directed set $\Lambda$ and a net $(T_\lambda)_{\lambda\in\Lambda}$ of maps from $P(A)$ converging to a map $T$. We have to show that $T\in P(A)$. Take any neighbourhood $O$ of zero in $A$ and a bounded subset $B$ of $A$. Since the addition is continuous in $A$, then there exists a symmmetric neighbourhood $U$ of zero (i.e., for every $u\in U$ also $-u\in U$) in $A$ such that $U+U\subset O$. As $(T_\lambda)_{\lambda\in\Lambda}$ converges to $T$, there exists $\lambda_U\in\Lambda$ such that $T_\lambda(B)-T(B)\subset U$ for every $\lambda>\lambda_U$. Fix $\lambda_0\in\Lambda$ such that $\lambda_0>\lambda_U$. Since $U$ is symmetric, then also $T(B)-T_{\lambda_0}(B)\subset U$. As $T_{\lambda_0}$ is precompact, there exists a finite set $M$ such that $T_{\lambda_0}(B)\subset M+U$. Hence, $$T(B)\subset T_{\lambda_0}(B)+U\subset M+U+U\subset M+O.$$ Therefore, $T$ is also a precompact map and the set $P(A)$ is closed\break in $L(A)$.
\end{proof}
Although we did not cited all of the references in this template file, I will include the references so that You can see how the references should be presented. 
\begin{thebibliography}{99}
\bibitem{1} A. Ansari-Piri, A. Zohri, {\em Banach precompact elements of a complete metrizable topological algebra.}  Far East J. Math. Sci. (FJMS) {\b 32} (2009), no. 3, 329–-333.
\bibitem{2} U. N. Bassey, V. A. Babalola, {\em Factoring compact elements of Banach algebras.} Far East J. Math. Sci. (FJMS) {\bf 27} (2007), no. 3, 717–-728.
\bibitem{Kelley} J. L. Kelley, I. Namioka, {\em Linear topological spaces.} D. Van Nostrand Co., Inc., Princeton, N. J., 1963.
\bibitem{3} B. M. Ramadisha, V. A. Babalola, {\em Some results about Banach compact\break algebras.} Kragujevac J. Math. {\bf 26} (2004), 123–-128.
\bibitem{4} B. M. Ramadisha, V. A. Babalola, {\em Banach precompact elements of a locally $M$-convex $B_0$-algebra.} Kragujevac J. Math. {\bf 26} (2004), 129–-132. 
\bibitem{5} B. M. Ramadisha, V. A. Babalola, {\em Some results about Banach precompact elements of locally convex algebras.} Far East J. Math. Sci. (FJMS) {\bf 13} (2004), no. 3, 383–-386.
\end{thebibliography}
\end{document}