

Topology Encyclopedia 
  Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry. 
  The most basic division within topology is into pointset topology, which investigates such concepts as compactness, connectedness, countability, and algebraic topology, which investigates such concepts as homotopy, homology, and knot theory. 
  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 which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories. 
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