This paper is mainly concerned with a class of nonautonomous discrete systems (<i>X</i>,<i>f</i><sub>1,∞</sub>). New definitions of proximity relations and sensitivity in nonautonomous discrete systems are given. Some relations among <i>P</i>(<i>f</i><sub>1,∞</sub>), <i>L</i>(<i>f</i><sub>1,∞</sub>), <i>R</i>(<i>f</i><sub>1,∞</sub>), <i>S</i>(<i>f</i><sub>1,∞</sub>) and <i>P</i>(<i>f</i><sub>1,∞</sub>)(<i>x</i>) are derived. And some chaotic properties of <i>f</i><sub>1,∞</sub> are proved.
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