In mathematics, pointless topology (also called point-free or pointfree topology, or locale theory) is an approach to topology that avoids mentioning points. == Intuitively == Traditionally, a topological space consists of a set of points together with a topology, a system of subsets called open sets that with the operations of intersection and union forms a lattice with certain properties. Point-free topology is based on the concept of a "realistic spot" instead of a point without extent. Spots can be joined (forming a complete lattice) and if a spot meets a join of others it has to meet some...