General Concepts
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.
Read more about this topic: Pointless Topology
Famous quotes containing the words general and/or concepts:
“We have wasted our spirit in the regions of the abstract and general just as the monks let it wither in the world of prayer and contemplation.”
—Alexander Herzen (1812–1870)
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