Page "Grothendieck topology" Paragraph 2
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Wikipedia
There is a natural way to associate a site to an ordinary topological space, and Grothendieck's theory is loosely regarded as a generalization of classical topology.
Under meager point-set hypotheses, namely sobriety, this is completely accurate — it is possible to recover a sober space from its associated site.
However simple examples such as the indiscrete topological space show that not all topological spaces can be expressed using Grothendieck topologies.
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