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Sierpinski space is the topological space
 with the topology given by
 .
Sierpinski space is  but not  . It is  because
 is the open set containing  but not  . It is not  because every open set  containing  (namely  ) contains  (in other words, there is no open set containing  but not containing  ).
Remark. From the Sierpinski space, one can construct many non-  spaces, simply by taking any set  with at least two elements, and take any non-empty proper subset
 , and set the topology
 on  by
 .
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