Pointless topology

In mathematics, pointless topology, also called point-free topology (or pointfree topology) or topology without points and locale theory, is an approach to topology where lattices of open sets are the primitive notion, and are not required to consist of subsets of points. In this approach it becomes possible to construct topologically interesting spaces from purely algebraic data. Points are then a derived notion rather than primitive, and there are non-trivial spaces that have no points.

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