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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.
Conversely, there are Grothendieck topologies which do not come from topological spaces.

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