<p>Let F: X x Y --&gt; Z. We say that F is continuous in each variabel separatel

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<p>Let F: X x Y --&gt; Z. We say that F is continuous in each variabel separately if for each <img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-201133152316343476135130403242971.gif" alt="" align="absmiddle" />&#160;in Y, the map</p>
<p>h: X --&gt; Z defined by<img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-20113315286343476132881706626790.gif" alt="" align="absmiddle" />is continuous, and for each&#160;<img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-201133152506343476137030520312162.gif" alt="" align="absmiddle" />in X, the map k: Y--&gt; Z defined by&#160;<img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-201133153516343476143168197699806.gif" alt="" align="absmiddle" />is continuous. Show that if F is continuous, then F is continuous in each variable separately.&#160;</p>

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