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\begin{document}
\title{Analiz k\i sa s\i nav\i\ 5}
\author{David Pierce, MSGS\"U}
\date{19 Mart 2012}
\maketitle\thispagestyle{empty}
%{\large \textbf{Analiz k\i sa s\i nav\i} (David Pierce), 20 \c Subat 2012}

$\tau$, $\R$ \"uzerinde \"Oklid topolojisi olsun ve
\begin{math}
\sigma=
\Bigl\{U\in\pow{\R}\colon\exists{\epsilon}\;
\bigl(\epsilon>0\land(-\epsilon,\epsilon)\included U\bigr)\Bigr\}
\cup\{\emptyset\} 
\end{math} 
olsun.

\begin{problem}
$\sigma$ k\"umesinin $\R$ \"uzerinde bir topoloji oldu\u gunu g\"osterin.
\end{problem}

\begin{problem}
$f\colon\R\to\R$ ve $f(0)=0$ olsun.
A\c sa\u g\i daki ko\c sullar\i n denk oldu\u gunu g\"osterin.
\begin{enumerate}[(i)]
\item
$(\R,\tau)$ uzay\i ndan ayn\i\ uzaya giden bir fonksiyon olarak $f$, $0$
  noktas\i nda s\"ureklidir. 
\item
$(\R,\sigma)$ uzay\i ndan ayn\i\ uzaya giden bir fonksiyon olarak $f$,
  s\"ureklidir. 
\end{enumerate}
\end{problem}

\end{document}
