In Grothendieck's work on the Weil conjectures, he introduced a new type of topology now called a Grothendieck topology. A topological space (in the ordinary sense) axiomatizes the notion of "nearness," making two points be nearby if and only if they lie in many of the same open sets. By contrast, a Grothendieck topology axiomatizes the notion of "covering". A covering of a space is a collection of subspaces that jointly contain all the information of the ambient space. Since sheaves are defined in terms of coverings, a Grothendieck topology can also be seen as an axiomatization of the theory of sheaves.