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<p>then under our second definition of the order, we have</p>

<p>
: if and only if  as <a href="page.php?w=prime_ideals">prime ideals</a> of the ring .</p>

<p>For the sake of consistency, for the remainder of this article we will take the first definition, that " is a specialization of " be written as . We then see that</p>

<p>
: if and only if  is contained in all <a href="page.php?w=closed_set">closed set</a>s that contain  and<br/>
: if and only if  is contained in all <a href="page.php?w=open_set">open set</a>s that contain .</p>

<p>These</p><p>
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