
 Hausdorff space  Wikipedia, the free encyclopedia (Site not responding. Last check: 20071019) 
  space, or separated space, iff, given any distinct points x and y, there are a neighbourhood U of x and a neighbourhood V of y that are disjoint. 
  In contrast, nonpreregular spaces are encountered much more frequently in abstract algebra and algebraic geometry, in particular as the Zariski topology on an algebraic variety or the spectrum of a ring. 
  Compact preregular spaces are normal, meaning that they satisfy Urysohn's lemma and the Tietze extension theorem and have partitions of unity subordinate to locally finite open covers. 
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