Generalizations
Occasionally, one needs to use the tools of topology but a "set of points" is not available. In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories that allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
Read more about this topic: Topology, Topology Topics