High Quality Content by WIKIPEDIA articles! In mathematics, pointless topology (also called point-free or pointfree topology) is an approach to topology which avoids the mentioning of points.Traditionally, a topological space consists of a set of points, together with a system of open sets. These open sets with the operations of intersection and union form a lattice with certain properties. Pointless topology then studies lattices like these abstractly, without reference to any underlying set of points. Since some of the so-defined lattices do not arise from topological spaces, one may see the category of pointless topological spaces, also called locales, as an extension of the category of ordinary topological spaces.

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