  We show that \emph{No unbounded profit with bounded risk} (NUPBR) implies
\emph{predictable uniform tightness} (P-UT), a boundedness property in the
Emery topology which has been introduced by C. Stricker \cite{S:85}. Combining
this insight with well known results from J. M\'emin and L. S{\l}ominski
\cite{MS:91} leads to a short variant of the proof of the fundamental theorem
of asset pricing initially proved by F. Delbaen and W. Schachermayer
\cite{DS:94}. The results are formulated in the general setting of admissible
portfolio wealth processes as laid down by Y. Kabanov in \cite{kab:97}.
